There's a site called MAME Action Replay which does something like this, here is the URL:
One of the differences is that score, rather than time, is the main focus of this site. No slow-motion or anything is allowed; all games must be played according to Twin Galaxies rules (they even have special TG versions of MAME which disable pausing, savestates, and so on during recording). Also, the .inp's are not encoded into .avi's; rather, you must find the emulator version it was recorded with and use it to watch it.
However, one neat thing about this site is the leaderboard. It has a scoring system for 1st, 2nd, and so on for each individual game, and these are totaled up to produce the overall leaderboard. This is somewhat flawed, in that many arcade games have multiple versions which play identically to each other, but I still think it's cool. =)
Among the .inp's that I would most recommend (provided you can find all the various MAME versions needed) are BBH's Shock Troopers, any of SPELUNKER's replays of the Double Dragon series, and virtually anything by Japanese players.