Well if you want to go that far, then all the games you'd consider Mario games are actually Donkey Kong games.
Actually, I'd be more inclined to say Donkey Kong games are Mario games.
But the "Oh, look! Not another Mario Game because it doesn't feature Mario!" is missing the point. It's not that these fans don't want another game where the main character is Mario - its that they want new and exciting ways to play. Splatoon does that. Captain Toad is more of what we got in 3D World. Yarn Yoshi is more Yoshi's Island (which, it seems, everyone's been disappointed with every previous attempt to revive that concept). That's not to say these games look bad. Hell, Captain Toad is probably going to be a Day-One purchase for me.
"Mario" stands for a lot of things - and in this case, when fans say they're tired of Mario games, they mean they're tired of more of the same. This doesn't mean "the same" is bad - it just means they're tired of eating pizza and Chinese take out and want to try the new BBQ place down the block.
Now, I don't mind more Mario games. I like them. I want them. But I understand folks what folks who say they're tired of Mario games really mean - but it's apparent from this that Nintendo doesn't.
Ehhh, I dunno. I totally agree with your assessment of Yoshi. As someone who doesn't care for Yoshi's Island, though, but really liked Yoshi's Story, and loved Kirby's Epic Yarn, I've gotten sold on Wooly World, almost against my will.
I think overall with this E3 Nintendo has sort of clarified what their ethos is all about, and of course there's going to be a lot of Mario in there. As far as Nintendo not understanding how to handle that, though, I had a different impression. Captain Toad is just a completely new kind of thing. It's Mario in a broad sense, but the Toad levels stood out in 3D World for a reason. Of anything coming out anytime soon, I'm weirdly most excited for Treasure Tracker. Those levels in 3D World felt like they were cooking up a new recipe in much the same way that Mario Galaxy paved the way for Galaxy 2, one of the best things ever made. And the a cappella challenges in Sunshine feel the same way in relation to Galaxy and 3D World. Obviously Cap'n Toad isn't going to be on the same scale, but it's fresh and interesting to me.
Mario Maker even seems to be like an extension of their art-creation angle which occupied the DS for a time. Again, Mario branded, but the actual product is pretty unique in Nintendo's catalogue, but also an extension of previous ideas.
What would've been worrying is if Nintendo had spent 20 minutes on New Peach U and/or Luigi 3D World DLC packs. It seems like we're done with mainline 2D or 3D Mario games for the rest of the current console and handheld generation. And instead of coughing into their fist, Nintendo is sticking to their guns. This probably won't have a huge effect on the WiiU's success, but I'm pleased to see the commitment to an overall aesthetically driven enterprise.