Genre-bending

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