Within one of the header files for the Alien Swarm SDK are Linux references to the windowing code (read: not for the server). A copy of the portion of the source header file is available from the Steam Forums.
#elif defined( PLATFORM_LINUX )
#define DEFINE_WINDOWED_APPLICATION_OBJECT_GLOBALVAR( _globalVarName ) \
int main( int argc, char **argv ) \
extern int ValveLinuxWindowedMain( int argc, char **argv, CAppSystemGroup *pAppSystemGroup ); \
return ValveLinuxWindowedMain( argc, argv, &_globalVarName ); \
But this isn't as exciting as the Steam Linux client partially running or the undiscovered cards yet.
Here's how Valve describes Alien Swarm in their Steam Store for those interested:
Alien Swarm is a game and Source SDK release from a group of talented designers at Valve who were hired from the Mod community.
Available free of charge, the game thrusts players into an epic bug hunt featuring a unique blend of co-op play and squad-level tactics. With your friends, form a squad of four distinct IAF Marine classes. Plan your attack using an unlockable arsenal of weapons with countless loadout configurations against a wide variety of aliens. Blaze your way through an overrun, off-world colony, eradicating the alien infestation in environments ranging from the icy planet's surface, to a subterranean lava-flooded mining facility.
For now though you can run Alien Swarm under Wine.