You need to broaden your definition. Desktops, laptops and Macs are all PCs.
/Agree
IMO - Most new phones and tablets would also fall under the "personal computer" designation.
To the OP: While there are laptops that do gaming better then other laptops, no laptop will compete with a good desktop. For myself I would only game on a full system. Being able to upgrade the graphics card is to important to me.
Laptops have design choices based around saving power and space both of those considerations go against speed.
I have heard good things about Alienware however if a laptop is needed for other reasons like portability. A machine that will game well will also get much less battery time and be heavier. Be prepared to always be looking for power sockets.
With 3k you could do both, make a decent gaming rig and buy a low end, but decent, laptop for portability.
Without knowing specifically what needs you would have beyond (I am assuming) playing Skyrim it would be not so easy to make recommendations for specific hardware.