Maybe it is just me, but... publishing a game that uses a mechanic seems easy enough, but publishing a mechanic alone... how are we expected to do so? As in, do we just publish a letter with some rules, or a video showing the mechanics off, or a game that uses the mechanics? Bit confused here.

You are absolutely free. The jam is primarily designed for role-playing games, but the participation of any other type of game is contemplated and encouraged. A text explaining how the mechanics work or a video showing it in detail is fine.

make a game with that mechanic being the core mechanic