If Yoshi gets his own recurring cast, including his own villain, then maybe I'll buy into this a little bit more.
I was just mentally comparing Yoshi's Island, Luigi's Mansion and Wario Land...
Luigi's Mansion is
very different in gameplay to Super Mario, but still it wears it's Mario roots on it's sleeve, the villain is King Boo; E. Gadd makes occasional appearances in other Mario titles (mostly ones that came out around the same time). Mario even appears in person in his most well known look. The unique elements to Luigi's Mansion (i.e. the non-Boo ghosts) stay in Luigi's Mansion.
Wario Land got increasingly different from Super Mario as time went on, Mario only makes
one appearance at the very end of the first game (and in only one ending at that). All the enemies and bosses are entirely unique (and in later titles, can get
very strange). No characters from Wario Land appear in mainline Mario titles, not even Wario himself. Basically by the time of Wario Land 4 the only thing Wario Land and Super Mario shared was that they were both Platformers starring Italian guys in coloured overalls.
Yoshi's Island is closely tied to Mario, sharing the same genre, but experimenting with it's aesthetics. It borrows a
lot from Mario, including characters and enemies, though it still has unique characters occasionally. Like Luigi's Mansion, unique elements to Yoshi's Island stay in Yoshi's Island, but unlike Luigi's Mansion, certain non-unique elements have actually bled back
into Mario (such as the idea of Kamek powering Bowser up, and Bowser Jr. looking like his father did as a baby).