The singleplayer arcade title demands the PS3 be connected and online, otherwise there's no play time. The Xbox 360 version is unaffected.
We could slip in a Ubisoft PC DRM jibe here but we won't, promise. Users starting complaining that without an active PSN account they can't play the excellent retro awesomeness of Final Fight: Double Impact on the console.
The "Sign into PlayStation Network. (80029516)" error message appears for those who want to play singleplayer or even local multiplayer. The Xbox Live Arcade version appears to be missing this Ubi-lievable cock-up (oops, broke my promise).
Neither Sony nor Capcom have offered comment but should we start running wild with speculation that all PS3 games from Capcom will demand Internet now? Nah.