Cheap off the shelf gaming computer?

Not as far as I can tell.
Best Buy offers several desktops with integrated graphics, as do retailers like Target, Wal-Mart, etc.

Um, yes? I have never encountered a DVD drive or RAM that weren’t discrete components. There are however many motherboards with integrated graphics.

Edit: On desktops, I don’t pay much attention to laptops.

Really? Huh. It’s just that I assumed that since graphic cards were ubiquitous here, it would be the same in the U.S. My mistake.