There are

In 2015 the total of third party software sales (combining all platforms) were north 27 million

In 2021, those numbers are behind 16 million 

Besides that. I don't know for bow long we will be able to keep this narrative JP third parties aren't releasing their games on Switch. The only game that aren't release on Switch are the ones that absolutely can't run on Switch. Games like Resident Evil Village and Monster Hunter World that don't even need to hit big in Japan in first place because their popularity worldwide is enough to offset any decrease in interest on their home market. Indeed those are games that NEED to be popular overseas to become financially profitable

Third parties are releasing their games on Switch. They simply don't sell as much as they used to sell when Playstation platforms were relevant. In past they have to have Nintendo platforms and Playstation platforms to sell, now they only have Nintendo's 

But I agree partially with your point that Sony outright ignoring Japan is the reason behind the overall third party market decline. Just disagree Switch is a path to revive third parties. 

Sony first party output in Japan was pretty irrelevant, so Playstation ecosystem was dedicated to third parties. On Nintendo ecosystem they have competition with Nintendo IPs and of course Nintendo will advertise and prioritize their own software, third parties will have harder time selling on Switch then they used to on Playstation.  

Switch is preventing the JP market to shrink, yes, but their own first party output keeps representing half of boxed sales and I don't see this changing in future 

"Dark ages of Nintendomination" is a statement that is plain stupid. If you look at the sales of individual Switch third party games, the vast majority of them are either flat or up in comparison to their respective predecessor. Then there's this graph which shows a clear upwards trend in response to growing investment in Switch game development by third parties:

None of the third parties that are supporting Switch are hurting. Their finances have seen a positive development or at the very least they've avoided sinking with the PS ship.

Part of the decline in overall third party software sales is due to this being a physical-only chart, but another important factor is that the overall number of game releases has decreased due to higher development costs, and as a result, publishers have focused more on proven IPs for the fewer games they make.

Let me clarify.  There is not a real decline on Nintendo systems since Generation 8, but there is a decline on Sony systems.  Third parties didn't really support Switch during launch, but third party sales have been steadily increasing on Switch ever since.  I expect, in a few years, if we compare total third party sales in Japan on 3DS and Switch, the Switch will have noticeably bigger sales.

The decline in third party sales overall is due to Sony not having a viable system in Japan anymore.  Some of these games/franchises that supported Playstation in the past are now transitioning to Switch and still more will likely release on Switch in the near future.  However, there are other franchises like Final Fantasy.  FF16 is not coming to Switch and I don't expect FF17 to come to a Nintendo system either.  This used to be a huge franchise in Japan, but it continues to shrink and shrink.  These types of games that are going to stick to Playstation are going to be recorded as a loss to third party sales in Japan.  Sony doesn't have a viable platform in Japan anymore.  That is where the loss is coming from.  Elden Ring is going to sell 20m copies worldwide at a bare minimum (maybe even 30m+).  How many third party Japanese games sell like this?  It's bigger than any Final Fantasy, and it's a Japanese game.  Shouldn't it be selling even better in Japan than it is?  These sales in Japan are low for a game like Elden Ring, because Sony just doesn't have a viable platform there anymore.  In order for third party sales in Japan to stay high overall, a game like Elden Ring would have to come to a Nintendo system.

"But I agree partially with your point that Sony outright ignoring Japan is the reason behind the overall third party market decline. Just disagree Switch is a path to revive third parties."

We may have to agree to disagree.  But I very much reject the idea that third parties cannot compete with Nintendo on their own system.  The reality is that third party games compete with Nintendo when they are on Playstation.  And so games like Final Fantasy are just not going to sell like they used to because they are on Playstation.  Nintendo isn't trying to compete with third party games.  They are trying to compete with Playstation.  (And they are winning by a landslide.)  Meanwhile, when an actual killer third party game does release on Switch, like Monster Hunter Rise, it sells great.  The main reason that third party games can't compete is that they are on the wrong platform.

Furthermore, the main big franchises that Nintendo gets on their platforms are Monster Hunter and Dragon Quest.  Every time one of these games releases on a Nintendo system, we see a crapload of time invested into these games on Nintendo Directs.  I just don't see how Nintendo is giving these big games the shaft.  If some other big franchises were to release their game on the Switch, I bet Nintendo would give them some good marketing too.

Rol and Kakadu already said most of what I was going to say, so I'll second them, as well as adding that its hardly Nintendo's fault if third parties and Sony are out of touch with the domestic market.

Appealing to Japan and the West are not mutually exclusive; Nintendo proves its perfectly possible to make games that do both. Sony and a lot of third parties are simply doing a piss poor job of it these days.

I think this is a overstatement. Some kind of games have cross appeal yes, but is natural to expect gamers sith very different habits and backgrounds will have different expectations and tastes. Nintendo have IPs that are historically stronger in Japan than elsewhere and conversely IPs stronger in West compared to Japan (of course keeping market size in mind)

However Nintendo have a HUGE amount of IPs and money to afford keep them floating even if they aren't very prolific. Some IPs will be huge in USA, some will be in Japan, some will be in both, but in the end it will translate in succes for Nintendo's ecosystem 

Bigger third parties like Square en Capcom can afford that as well, but ghe bottom line is most of third parties simply don't have that huge amount of IPs or resources to keep enough games to appease to both markets. I don't even understand why exactly Japanese people expect from older IPs these days. Take RE 2 remake, it's a perfect well crafted remake, faithful to the original, focused on the horror, solving puzzles and exploration. It was released in HD with very great graphics and does everything a remake needs right.

It sold 10 million copies worldwide but barley half million in Japan. The original sold over 2 million copies in Japan and is among the all time third party best seller hall

I doubt anybody will have the nerve to say Capcom did a piss poor job with RE 2 remake

What happened then? Well, some might think there was a shift in interest and tastes among Japanese gamers who now prefer portable games and/or games that have portable gaming elements so a RE 2 remake is by definition absent of any chances of having a Japanese breaktrough regardless of how good a job Capcom could possibly do

Except by the games that can't run on Switch (Capcom, Square, etc) it has been a while most of games are released on both Switch and Playstation. There is an almost perfect transition from PS4 third party sales to Switch third party sales on going since Switch found success 

However those sales are still pale compared to that they used to be years ago (3DS/Vita/PS3). The graphs were clear, third party sales are declining while Nintendo first party are growing. PS4 third party sales were also smaller than PS3 third party sales, while Switch is barely earning the third party sales they already owned on 3DS

In the end, the truth is most of people buy primarily Nintendo games on Nintendo platforms, thats why third party split for Nintendo was always smaller than Playstation's (or conversely, you can state first party split was just far smaller on PS4), hence why a market where there is only Switch with relevance is further reducing the importance of third parties.

This is concerning for the future of the market and as Japan is the second most prolific market to create games this is likely to affect the output of games, with Japanese third party having even hard time to keep competitive with technology as they have no money to compete fairly not even with Nintendo games that are arguably smaller budget compared to western games 

Thankfully JP devs are finding a way to sell their games outside Japan, that's can save them from this dark ages of Nintendo domination. 

The 3rd party games sales declined on PS is Nin's fault and not Sony's fault??? Almost sound like a big fan of Sony.

Ghost of Tsushima did pretty well in Japan and worldwide.

Is Sony's fault of course, but don't change the point is their dark age. 

That's a very good point that I've missed. The number of games released are decreasing, and sales are decreasing as well

To say this is not a dark age though, it's overlook the data, Switch is barely recovering the market lost by 3DS and still far from recover tonthe point they were when there was more systems in the market. You may just say you don't care for situation of third parties, but they never presented themselves in worse state than they are currently, at least since PS1 days

You are missing a point of how Playstation absence is detrimental for third parties. Playstation first party is irrelevant in Japan, all customers locked on Playstation ecosystem therefore buy, overwhelmingly, third party games. This alone push Third party sales towards bigger peaks on PlayStation platforms compared to Nintendo's. Switch is the pretty much the second most successful console of all time in Japan and has yet to beat third party sales of only mildly successful consoles likes Vita and PS4

The growth of Switch ecosystem, while increase third party sales, will also reflect on Nintendo's first party output, the growth in userbase is shared because, unlike Sony, Nintendo first party output is truly competitive and just keep getting stronger as result of Switch's success 

An workaround for this is, of course, go multiplat, release on PCs and invest in localization to USA and Europe. If those third parties look for Switch as their only way to recover they following the path to shrink and becoming les relevant. Barely flat sales generation to generation when development costs rises is at best an orange flag, they will need to find other way to increase their revenue which, of course, includes keep supporting Playstation and expecting their recover, or, at least, keep their fandom outside their home market