Solid specs for a laptop. The 6770M is a very good laptop gpu, and as you said this is basically a desktop replacement, I'm assuming it should be plugged in most the time anyway. Even the most effecient laptop isn't going to have the best battery life when gaming, so that shouldn't be a problem.
For me personally though, I think the screen quality is a bit on the lower end, which I think HP had to use to counter the GPU its using for the asking price. But I'm very picky when it comes to monitors and the likes.
The only game I've tested however was Dragon Age 2 with all settings on Medium, as I didn't want to run it on Dx11 due to poor optimization, and it ran beautifullu. Skyrim should be playable at medium settings I'm guessing.
The laptop I used had a 2410M processor which is stronger but shouldn't change things too much. Be happy with the laptop. Its got a well balanced spec, and looks great to boot. I would be happy if I were you =D
