What do you mean, "Doki Doki Panic was actually a Mario game from the start"? I always heard the opposite: that is was rebranded as a Mario game when it reached the USA.
Basically they first made a Super Mario game(which was very different), and it became Doki Doki Panic. Then, later on, when it was brought to the US, it was effectively reverted back to being a Super Mario game.
For some reason I can't find the proper source anymore, though. That said, I'll leave off the conversation part since I can't legitimately source it. I heard the original as you did too.
It's "official", sure, but does that means than it is "important" or "serious"? How much thought was put into this, and by whom? From my point of view, this looks like an add, no more no less. Besides, the page itself never mentions the words "main", "mainline" or "canon": the video just presents "some of Mario’s greatest hits" and the article talks about "Mario’s many adventures", which is a broad term: if Mario Maker is an "adventure", then shouldn't the Mario Party and most of the Tennis and Golf be considered as such? Some of them have stories just as "adventurous" as the Mario Maker's, I think. It doesn't say anything about "plateformers" either.
I also wonder why New Super Mario Bros. Deluxe is there, but not Mario 64 DS. My guess is: it's for marketing purpose. There is no point for Nintendo to promote an old DS remake, but a Switch remake still available at the moment? Yeah, let's put it on the website and present it like it's important.
The actual original version of the website listed it as "these are the mainline games" and listed all the current ones, bar ones not released yet(Bowser's Fury and Super Mario 3D All-Stars at least, maybe some others). They changed the website entirely from the old design. My guess is they realized it was a poor way to put it, and that they just consider these "important enough" or something like that.
I completely agree with you, that said. It's arbitrary, regardless of being official. There's no reason not to include both versions of Super Mario Bros. 2 in general. They're both clearly core games, like the rest of the platformers. It makes sense not to list the later Wario games, just as well. The only one that could be listed is Super Mario Land II, of course.
For the most part, it's clear they don't take it that seriously either. Mario Kart is practically a core series for them too, essentially being hyper popular and a place to return tons of characters. It's the only series they dared to make into a Gacha too. And get another full Arcade version. It's clearly pretty special in some ways. I mean, still a spin-off, but yeah.
If it makes you feel better, Pokemon is odd with it too. The Let's Go series of games are considered mainline... along with the regular series. Despite being beyond different outside of just being another re-telling of Gen 1. Notably the gameplay is massively changed up from the norm with how catching even works, making it much closer to a spin-off. They never did anything besides updating mechanics at most otherwise in the mainline Pokemon games. Obviously balance changes too, but they never outright changed any core mechanics till now. Then again, the remakes are mainline and their own timeline too, so there's basically 3 different timelines that are all mainline. Confusing isn't it? Companies are just weird on what they consider mainline. And don't get me started on what counts as canon or not. D: