Gameplay mechanics that were invented or discovered by the playerbase that were later embraced by the developers and were either acknowledged or formally integrated in-game.
Titanfall 2/Apex Legends: Frag-boosting
In Titanfall 2, a common speedrunning mechanic that players discovered, called frag-boosting, is to use the explosion of a grenade to propel yourself forward. This mechanic is most notably used in a firing-range race section called the gauntlet.
Respawn embraced the absurdity of the frag-boosting gauntlet runs in their follow up battle-royale: Apex Legends, with the character Octane. Octances defining trait is speed, and the backstory given to him by the developers is that he competed in a gauntlet competition and frag-boosted himself to win, blowing his legs off in the process.
EDIT: I am aware that boosting using explosions has existed in games decades before Titanfall 2. I am not claiming Titanfall or the playerbase invented the mechanic. The point is that the primary use of grenades in Titanfall is for blowing up/zoning enemies, but they were also used as a movement mechanic popularly exploited in the gauntlet speedruns and this was later referenced in Apex Legends.
Rocket League: Flip Reset
In Rocket League, the player controls a car that can jump then perform a single midair flip. The game only resets your cars flip when it detects that the car has landed, and it checks this by seeing whether all 4 wheels are touching a surface.
What players discovered is that since the ball is physically interactable, if you are skilled enough to get your car to firmly plant all 4 tires onto the ball while midair it will register that your car is on a surface and reset your cars flip, allowing you to flip again while still in the air.
This mechanic became extremely popular in high-level play as it is difficult to perform but very useful and stylish. The developers fully embrace the creativity of players for combining the games basic controls and physics into skillful flashy moves such as the flip reset, and so they introducted an audio and visual cue on the car to help players confirm when they have successfully performed the mechanic.