Yes, they are. And, despite their assertions to the contrary, they always have been. Remember, the first Playstation was a revenge console. They have always been going at it, albeit in different ways.

And if the new Switch is powerful enough, things will REALLY get interesting.

What a poor analogy. I'll help you understand what is MARKET competition by using your base of reasoning...

If people are having thoughts choosing on which thing to fly, you could add a hot air balloon to the mix, you would still have a competition, because they are spliting the audience of flying enthusiasts

I think your problem is to think that competition is a power showcase where we have gladiators fighting each other in a arena to have one remaining... thats not how it works

Competition =/= Tournament

It makes sense to say Switch or PS5 is crushing Xbox because they are but, saying Switch is crushing PS5 is crazy and delusional. It's also very strange to just disregard selling 4 million consoles in a month alone like it's nothing and it's irrelevant. You have to sell the consoles to sell the games  

They're both competing for people in the dedicated console market.

To a lesser extent, they're competing with the universal media/communication machines, like iPads, mobile phones, Smart TV, and PCs.

To an even lesser extent, they're competing with other forms of media such as YouTube and Netflix-style streaming services.

On the arguments you made. I find some considerable problems with them. First, I find the arguments in favour fall short of what they could achieve:

On the first batch:

1. This encompasses multiple points, but I don't think you make the strongest cases you can with these arguments because it's not only that they make hardware. Dedicated console purchasers are a specific market niche. The differing features don't change that.

2. "Core gamers" isn't a niche. This is a pretentious term used by insecure gamers and marketing people to try and artificially make certain gaming habits/games look more important. You can call it a species of gimmick, in other words.

Second, I find the arguments against to be evasive of the relevant point or are straight-up non-sequiturs (pointing out a fact that doesn't make the proposed argument):

1. The fact that Switch is a hybrid console while PS5 is strictly a home console is a great argument for why Switch is more successful, but it doesn't make any kind of argument that they aren't in competition with each other. All the lifting is done by "they have different features" while ignoring the similarities in an attempt to make it look like a valid argument. For example, you wouldn't say that Tesla isn't in competition with General Motors simply because Tesla focuses on EVs while GM focuses on gas-powered vehicles.

2. Arguing that people own both consoles is just pointing out a fact; it isn't an argument that they aren't in competition with each other. Owning products of competing brands is common in most niches. If someone uses toothpastes of different brands, it doesn't mean those brands don't compete. In fact, this is better at making the opposite argument as it means that purchasers are indeed weighing in on what system to buy games for and what system to play games on.

3. Metallica vs Taylor Swift are specific products akin to Animal Crossing versus Call of Duty. While you say they don't compete, their record labels Universal and Warner Bros certainly do compete with each other, and the various platforms that play their music, like Apple Music and Spotify, certainly do compete with each other.

4. I'll add that they target the same niches in advertising and communities; and advertise on the same media platforms and sub-categories, the same trade shows, and the same magazines/e-zines. Website communities (like this one) are most often for both Nintendo and PlayStation gamers with strong numbers from both fanbases, while PC/mobile discussion is often considerably less.

5. And I'll add another: they compete for exclusive content specific to the dedicated console arena; they're constantly courting the same third-party developers to release their content on one platform, not the other. Sony and Nintendo are territorial against each other. If anything, Microsoft is the one who is less competitive on this front.

Yes. Tho one can make the argument that their target markets do have their diferences, they also overlap a lot. So yes, its competition.

"Sony and Nintendo are in competition.  But are they really?"

It depends on who is winning.  During the PS1 & PS2 era, Sony was winning and "the internet" declared they were competing.  Since then, Nintendo has been winning, and "the internet" declared they were not competing.  If Sony can get the upper hand again, then they will be declared to be competing again.

Depends on what you consider crushing. PS5 could sale as much as 120 million depending on when Sony launches PS6. Currently PS5 is tracking behind PS4, which sold less than 120 but PS5 could remain on the market without a successor longer than PS4 allowing PS5 to hit 120 million. Switch is looking to reach the coveted 160 million or even higher. That puts Switch 40 million above PS5, I personally think that should qualify as getting beat and atleast approaching getting crushed. So no, not really delusional just depends on your definition. This is supposedly a market leader (PS).

The Switch obviously is not selling more than the PS5 right now, it's a dying console that's going to be replaced this year. If you make a launch aligned comparison the Switch will be ahead every year, I guess, but I'm not sure.

At the end of the day, when it's all said and done the PS5 won't sell the same as the Switch, but right now Sony is selling more consoles.

Because they get way more money from selling more first party games then 2nd and third-party games. All the profits from first party games goes directly to Nintendo.  Plus, they can license their own IP's to get even more money they can't do that with any third-party games.  Again, Nintendo makes way more money than Sony from first party games and on top of that they make way more money than Sony from licensing their first party IP.  There is a mega ton of Nintendo merchandise that generates money for Nintendo and there is almost next to no merchandise that is based on Sony video games.

It is because the PS5 is still tracking slightly behind the PS4 and the Switch already sold 30 million more units than the PS4.