Following series initially won't require any special things from your laptop.
A bit later you'll probably want better CPU and 4 cores at least. Otherwise it will a bit painful to run it because game will run too slowly because of software renderer.
Later, as mrmixer alreadhy says, Casey switches to use OpenGL then you'll want laptop that supports at least OpenGL 3.3 core profile - for any recent laptop this should not be an issue. Graphics card performance should not matter much, I think you should be able to run anything even on Intel GPU.
Once he switches to using OpenGL is the 4 core thing still a desire, or will that make it much easier to run on 2?