I don't think there are too many broad genres they don't have a franchise in tbh
Platformer - Mario, Yoshi, Kirby
Racing - Mario Kart/F-Zero
Shooter - Splatoon
Action/Adventure - Zelda/Metroid
RPG - Pokemon
Puzzle - Captain Toad
Arcade Shooter - Starfox
RTS - Pikmin
Life sim - Animal Crossing
Sports - Mario Golf/Strikers
Party - Mario Party
Some kind of openworld game would be new for them I guess, although Zelda U should have that covered