The stock is what throws me off.
The rifle pictured by the OP is a .308 built by George and the boys at GAP. While Mr. Kyle prefered a .300 or .338 there should be no questioning the fact he's holding a short action in this pic.
My sis got me his book some time back. Haven't looked at the first page.
Silly I guess, but with his passing I think I'll wait a little while before I read it.