An arena shooter where your opponents aren't AI-controlled nor other players competing against you, but rather the ghosts of other players who are moving around the same area and shooting at the ghosts of other players. Yes.
Hell Is Other People takes the idea of an asynchronous multiplayer game. That is, you're playing against other people, but not at the same time. When you start, it randomly spawns a ghost opponent, in reality a recording of a previous player. As you progress, it spawns in more and more ghosts, all of whom are merely re-enacting the motions of past players' efforts to shoot down the ghosts they faced.
Every player is denoted by a three letter name, so you may even spot yourself appearing as a ghost in your own game. Keep an eye out for "DJW" while you're in there.
One question before I go though: who did the first player fight against?
Hell Is Other People [George Buckenham]