When playing word games, it is important to not get the game turned around on you.
OK, so let's say the game warden wants to play along with you on the carbine vs rifle thing. You want your carbine to be a pistol because it uses pistol cartridges, right? OK.
1- The 45 ACP cartridge in a pistol is not legal for hunting in most states.
2- Most states define a pistol cartridge legal for hunting as being longer than xx inches or having more than xxx ft-lbs.
3- If it is a pistol, you could be cited for having a weapon in violation of the NFA, which prohibits pistols with barrels over a certain length (16" if I remember correctly).
4- If you Google the word "carbine", you will find it refers to a short rifle.
Save yourself headaches and heartache and don't play games.