Okay, so I bothered looking at it again... the rounds look bigger than I remembered em the first time. Upon closer examination, I'd say it's a McMillan 50 with a thumbhole stock.
A few screeshots for comparison:
(
Also notice the slight goof: one scene he's shown taking the top round, but a moment later when he's shooting it's the bottom round that's been removed.)
And here's a McMillan 50 with the thumbhole stock:
http://www.bawo-custom-guns.de/impress.html
And an AI AW-50 on a similar angle as the movie screenshot, clearly not the same gun: