An “experimental” gameplay is not necessarily outlandish, genre-defining or genre-defying (e.g. Katamari).
A lot of developers created innovative games starting from an establish gameplay or genre. This is often referred as “adding a twist” but sometimes a relatively simple twist completely transforms the entire experience.
Here are some notable examples roughly following the templates you researched.
What are the twists and what are the effects on the “traditional” gameplay?
2d Platformer
Braid
Fez
Starseed pilgrim
VVVVVV
Super Crate Box
FPS
Aside of narrative/exploration games
Scale
Museum of Simulation Technology
Mirror Moon
Super hot
Screen Cheat
shmup
Warning forever
Captain forever
Lovers in a dangerous spacetime
Pixel junk shooter
Toughcoded
3rd person platformer action/adventure
Grow Home
Journey
Shelter
Beyond Eyes
Tiny & Big in Grandpa’s leftovers
Flight sim
Flower
Oases
Innerspace
Exo One (not out yet)
2d zeldalike/RPG
Undertale
Minit
Hack ‘n’ Slash
Crawl
Crypt of the NecroDancer
Driving games
Beware
My summer car
Roadeo
Absolute drift
Perfect stride