I was curious if all-in-ones even offered graphics with discrete video memory.
They're essentially the same as laptops. They can either have Intel graphics or have a video card (usually a "mobile" version, like a laptop). Some all-in-one video cards have discrete video memory. For example some of ***Dell's 27" all-in-ones***
have NVIDIA GeForce GT 640M 2GB GDDR5. The least expensive is $1599.99.
At HP, you had to go up to the $1,060 model to get dedicated video memory. The rest were all integrated graphics with shared memory. One that was less than $1,000 had 6 GB of RAM and an Nvidia 610M, but I don't know if that would be good for gaming. Maybe it depends on what kind of gaming you do.
An Nvidia 610M is probably OK for most casual games, though it might be sluggish with some. It's not appreciably better than Intel graphics.