3413GT is heavily modified; it started out as a Series I, was upgraded to Series II spec, then additionally given the 250LM roofline, then received a modified front end for brake cooling... and so on and so forth.
The GTO in the game is a regular Series I, which the game claims is 3729GT (although it's wearing the plate of Nick Mason's 3757GT). Except for being RHD (from the factory, as it happens), and originally white (Bianco), it's pretty standard.
I think the game is incorrect. #3729 is (or was?) white and has the race number 10. Nick Mason's car race number 22. Tom Price's GTO has the race number 20, and it is #3943. Unless they repainted 3729 red with a race number that was already in use, I think the one in the game is #3943, belonging to Tom Price.