Is it possible to submit somebody else's run?

In what sense? As your own run? It is possible to add other people's runs as a moderator of a game if maybe they don't have an account or they just didn't submit it period and you want it on the board (but not as your own run of course)

He probably means old runs on youtube, I see many games with no runs yet there are videos on youtube.

Yes and no, you have to submit it as your own but you leave a note in the comment section the run is someone else's.

Timmiluvs: Because completion. I do it all the time.

http://www.speedrun.com/user/Distortion2 <-- that guy rarely submits his own runs to this website yet when someone else does it for him it always ends up under his name. So it definitely ¤can¤ be done.

emeraldaly: Game moderators can submit runs on other people's behalf. Other people can't (without what I mentioned above).

http://www.speedrun.com/run/8y85qowy

...no? ffleret isn't a mod for RE7

but moderators can edit runs to change the runner. I did the same thing before promotion

I think it is possible.