Why do some games get approved (Splix.io, Slither.io, etc) but very similar games (Little Big Snake) get denied for being 'endless, with arbitrary goals'? The majority of speed run categories are arbitrarily set to begin with.

Most categories aren’t arbitrary. Things like beating the final boss and getting all collectibles are clear objectives created by the developers.

So is attaining a certain score in a game as quickly as possible, a speedrun category I've seen in NUMEROUS games here.

Most of the games you are talking about got accepted when the game request rules where less strict.

I suppose that explains things then.

though its more rare to get rejected than its to get accepted nowadays

It will depend on the game developer's perceived goal. Some games will be denied because the developer's goal isn't clear, or as you said, endless. For speedruns, you need a clear end goal or finish line.