I always thought a Cloverfield/big monster FPS would be coo'. It'd be like GTA and Battlefield rolled into one. I guess your only goal would be to keep the the big guy/gal away from randomly generated critical locations and safe zones for as long as you can. I suppose the main draw to the game would be the atmosphere and the whole "no two playthroughs are the same" thing like Routine and Dear Esther since it would have to take place after the city was evacuated.
Achieved with Garry's Mod and Photoshop