Yoshi's Island was left off the list last time too. I think it has more to do with the evolution flowing more naturally from Super Mario World to Super Mario 64. Yoshi's Island looks odd with its cartoonish artstyle and baby Mario.
Super Mario Bros. 2 (The Lost Levels) is omitted from the Nintendo.com list, even though it first appeared in Super Mario Allstars in 1992, and has gotten a proper release since Wii Virtual Console.
Super Mario World 2: Yoshi's Island was released in time for Super Mario Bros. 10th anniversary (JPN August 1995, NA/EU October 1995) and Nintendo Power mentioned this in their preview in volume 75
“Super Mario Bros. fans, prepare to celebrate! Mr. Miyamoto and the EAD team have worked their magic once again, just in time for the 10th anniversary of the original Super Mario Bros. for the NES.
They’ve created an all-new adventure for Mario and Yoshi that breaks new ground in more ways than one. It’s not only the most technologically advanced Super Mario game ever - it uses the Super FX2 chip to create amazing scalling efffects and the most gigantic enemies you’ve ever seen - it’s a treat to behold…”
The English manual has a logo that says "Super Mario: Yoshi's Island" at the top of the pages. The Japanese title was "Super Mario: Yossy Island" (or "Super Mario: Yoshi Island")
http://gamesdbase.com/Media/SYSTEM/...World_2-_Yoshi-s_Island_-_1995_-_Nintendo.pdf
Super Mario World 2: Yoshi's Island is a Mario game starring Yoshi (like Castlevania: Symphony of the Night starring Alucard instead of a Belmont), while Yoshi's Story, Yoshi's Island DS (YI2), and Yoshi's New Island (YI3) are Yoshi games that spun off from Yoshi's Island.
Mario's Creators Answer Burning Questions About the Series - Game Informer Sept 2012
http://www.gameinformer.com/b/features/archive/2012/09/24/miyamoto-tezuka-interview.aspx
Here in the States, Yoshi’s Island was referred to as Super Mario World 2. Despite the title, many gamers don’t consider it part of the core series. Do you consider it part of the classic canon of Mario platformers or is it a spin-off in your mind since the player controls Yoshi?
Shigeru Miyamoto: When we first made Yoshi's Island, we considered it part of the Mario series. After that, the Yoshi series continued on its own. As developers, do we consider it to be part of the core Mario series? The answer is yes.
The way I see Yoshi's Island and Wario Land is that they were introduced in the series akin to "backdoor pilots" of spin-off shows (like NCIS LA/NCIS NO in NCIS, NCIS in JAG, The Flash in Arrow etc.) to hook people in before fully spinning off. It's a tricky situation.