Famitsu does not track Amazon but Media Create does.

I guess you could say Yoshi's appeal is ... dinosauric 

He was just so hungry he ate his own sales

Im trying to say that third party success on nintendo machines is always mediocre compared to succes of third party games on other consoles. Its really hard to be even as half as succesfull as nintendo is on their own platforms.

The success of third parties in Japan is actually competitive on Switch vs PS4.  Some games do less than PS4, others more, some even.  My Hero One's Justice for example did better on Switch.  Dragon Quest Builders 2 is pretty even.  And so on.  

One issue though is Switch gets some of these games late and that does impact sales. Also, some of these series have spent years ignoring Nintendo platforms entirely.  It will take time to build an audience on Nintendo systems just as it took time to build one on Sony systems.

The problem isn't third parties not selling as they normally do, it's Nintendo happening to control 5 or 6 of the most powerful IPs in Japan

That's understandable though, considering the quality of their games.

Also, just look at Sony this generation. Even CoD or Fifa are slowly having trouble keeping up saleswise to Spiderman or The Last of Us, for instance.

First party games are meant to attract gamers to your respective platform. And to achieve that, they need to make them as good as possible. The lack of such exclusives is why Microsoft couldn't hope to recover this gen and is the reason why Sony managed to catch up last gen.

Some third party titles/franchises are hugely popular, like the aforementioned CoD and Fifa. But with all the gaffes their publishers are doing to alienate their playerbase and milking them to death, I think that more and more players are avoiding those and look for the first party titles which are complete games at launch (I'm looking at you, Anthem! And all those other GaaS with long roadmaps and little initial content!) and don't try to rip you off at every corner, instead just being fun to play.

Rest in peace you great tracker you! Media create forever out!

You need to do your research.  There are quite a few 3rd party games that sold more on Switch than anywhere else.  Late release dates from being a new console have more to do with lower software sales than anything else.

And even if it does sell more on say PS4 or X1, the sales are still there for the developers to see profit.  And that is why more and more 3rd party releases are starting to come day and date with the other versions now.  Look at Wolfenstein New Blood, Mortal Kombat XI, DOOM Eternal, Crash Team Racing, Valkeria Chronicles 4, and Starlink as examples just off the top of my head.

Are Japanese sales numbers the only ones left on this site for software? If so, what happened?

Digital sales happened, making the total sales numbers increasingly wrong. So wrong by now, that they got dropped altogether, now just collecting shipment data.

Speaking of shipment data: Will those get added to the game pages? Would be nice to see at least the evolution of the official shipments of the games.