One cute thing I noticed in the pictures is that in the first one (after the header image) there's a cabinet full of Pokemon stuff. Top shelf has plush and figurines and middle shelf has the main series Pokemon games placed chronologically in order (though looks like they ran out out of room as it stops at BW2 and I don't see enough space for XY or SM) with also figurines of Pokemon from that gen (including those special figurines they gave out as pre-order bonuses). But then you look at the bottom shelf and though it's hard to tell what's being dispayed, there's something which is recognizable: A Jill plus from Drill Dozer. So it can be assumed that bottom shelf probably either has GF's other older games they made or those could also be prints of the magazines that GF made when it first was created. Shows even though they're now mostly known for Pokemon they do care where they came from and about the other games they made.
And not to mention all the Pokemon plushies that are around. We mostly saw Pikachu and the Substitute Doll but I can only imagine how many more there are lying around.
It's interesting how some of Game Freak's platform games aren't even available on Nintendo systems. If I recall correctly, Giga Wrecker was a PC game, and Tembo landed on PlayStation 3 or 4. If it weren't for its exclusivity, would Pokémon be more self-contained than it is now? The franchise refuses to cross over with other Nintendo franchises, such as Mario Kart 7 including Link, Inklings, and Animal Crossing characters, but not Pikachu or any other Pokémon. Smash doesn't really count, and most crossover games are just the gameplay with Pokémon slapped onto them, such as Mystery Dungeon, Pokken Tournament, Conquest, and even GO.
Hm, I don't know, that feels more of Nintendo's choice than GF's. Aside from Smash Bros, Nintendo stance on Pokemon seems to be that its the red-headed child of the family. In addition to the Mario Kart 8 exclusion, Animal Crossing has items based on many of Nintendo's popular franchises... except Pokemon. Mario Maker is a strange case too. By using the Amiibo you can have other game characters be "playable" in Mario Maker and they all come with a special sound effect relating to their franchise/game. And while Pokemon does have characters, the odd thing about them is that they don't have a special sound effect to them.
Now I have no idea what's the business side of things is like. Like does Nintendo need to pay GF (or rather, the Pokemon Company) to use Pokemon content? I wouldn't think so, they own 1/3rd of the Pokemon Company. Do they have to first submit an idea to be approved of from GF and the Pokemon Company in order to go ahead of using any Pokemon content? While I can see that slowing down the process of them including them in some things, I don't see why GF or the Pokemon Company wouldn't let them add in Pokemon content into Mario Kart, Animal Crossing, or give them sound effects for the Pokemon characters. To me, it always felt maybe Nintendo is jealous of Pokemon's success & popularity, a franchise made for their consoles yet they don't own full rights to it. You mention Mystery Dungeon, Pokken Tournament, Conquest, and GO, games which feel like Nintendo had very little say in the creation of aside from letting them make it for their consoles. The Pokemon Company were the ones who approached Bandai Namco, Tecmo Koei, and Niantic to develop Pokken, Conquest, and Go.
If Pokemon wasn't tied down my exclusivity, I'd actually think they'd be more out there than contained. When Nintendo finally relented on making Nintendo games or mobile devices Pokemon was one of the first to jump on board. And as pointed out, GF has made other games for other consoles and PC (which for a second party developer, while not unheard of, I would say is rare especially nowadays when publishers are more tight gripped on their developers).