Can you show me a rifle that you shot like that?
well, here's a http://media.midwayusa.com/ProductImages/Large/334907.jpg stock, which has a pistol grip but the stock is connected to it for legal reasons. Not like the rifle pictured but it's something I mentioned.
Here's a skeletal http://www.mississippiautoarms.com/images/stock.jpgwhere it's possible to wrap the thumb as pictured. Not that I would ever do it, but like I said, the animation is probably messed up a little bit.
But anyway, I really don't get your point. There is a pistol grip. You can SEE it, right there. Where the character chooses to put his thumb is irrelevant. In fallout 3 when you shot the BB and repeater rifles, you wrapped your fingers around the gun in such a way the sights would be blocked. Does that mean it's impossible? No... just some messed up animation, which is common in these games.
BTW, I am not arguing that it is a Barret or based off of Barret designs- it's clearly something different, and I've looked at 20 or so different AM rifle designs and can't find a single match, or anything approaching what it might be. I believe it's something obsidian cooked up by themselves.
Ok, there is a few possibilities of what that sniper rifle may be, you decide:
http://en.wikipedia.org/wiki/EDM_Arms_Windrunner
http://world.guns.ru/sniper/cheytac-0.jpg
http://en.wikipedia.org/wiki/Barrett_M82
I think it's the M82.
Doesn't look like any of those to me, least of all the M82. I think we need to stand back from this one and stop trying to classify it for a little while. Whatever this is, if it's not completely made up it's quite obscure.