We could add categories in relation to each of the arcade terminals and either make a certain number of points

Nope, Speedrun.com isn't a high score site, it's a fast time site. I'm not going to try and moderate that. Sorry.

Or else do a speedrun on the fastest to reach certain scores

(I'm just giving ideas)

it could be about doing X amounts of levels in the arcades, or reaching certain scores like in pacman.