Laptop gaming is laggy. Internet is fine. What?

First: Don't buy gaming laptops, they are a rip off.
Second: Try cleaning up your computer, and I don't mean the hardware. Download something like Ccleaner to get rid of trash, and do a virus scan to make sure that some third party software is not eating into your resources.

Check what other programs are running before you start up the games. Use the task manager to view the current CPU and memory usage levels.
I would recommend you close everything else including any programs running in the system tray (that bit in the bottom right with all the icons).
You say you have an Intel Core i7, but which one is it? Is it dual or quad core? Not every i7 is the same…

You say dedicated AMD video, if so, what model is it? A lot of systems come with integrated video (including AMD), but that does not mean "dedicated" video.
Integrated AMD video (on the processor chip) is very low end for any gaming. A discrete video with dedicated video ram (2GB or more) would be a lot better, but we just don't know what you really have.