Close enough - I'll be out the next few days, so best to keep this moving.
It's GTA4: The Ballad of Gay Tony (TBoGT)
1) Robot Chicken did a parody musical number called "The Ballad of Gay Tony". In it, Zangief sings about like to stick men between his crotch for a piledriver
2) Anthony = Tony! Also, both Anthony Bourdain and Gay Tony were big on using drugs, particularly cocaine
3) Cause enough damage/kill/break laws and the police/military come after you, a standard in most GTA4 games. In TBoGT, right before the final missions, one of your allies comes by in a helicopter and blows up a bunch of cars driven by Russians blocking your way
Unused:
4) I'm thuper, thankth for athking! - he's gay
5) I'm the owner of the hottest gay and straight club in Liberty City at the same time - direct quote from the game, mentions Liberty City, the location of where the game takes place
You're up, Sir Dicks-alot