If I knew a gamer who bragged to me like that, I'd try to get his statement on tape (like taping a gaming session or something) and turn them in to the cops or something.
That is pretty upsetting that there are gamers like that out there. Sure, there are all sorts of people, but I would want gamers to have a love for the game enough that they would hopefully support it.
Just a piece of advice states have different laws on people taping other people without their permission. Besides I don't think the cops would do anything they would have to have a complaint from the store or the person things were stolen from.
I did get one guy in trouble I knew he worked for the library and he was always stealing things from it like books, DVDs and such. I told my friend who is a head librarian at another branch who told his head librarian and they watched him until they caught him stealing.
Of course hearing this made me put my name in all my books and make a master list of where my books were going when leaving the house.