Is a desktop better then a laptop for gaming?
Generally speaking, at the same price, a full-size desktop will perform better than a laptop.
Would a laptop over heat?
Any computer can overheat for a number of reasons. Assuming a cool room, out of sunlight, not in a confined space, and no dust buildup in the laptop: no. I've had an Alienware 13 for a 19 months now, it runs absolutely fine.
Should I get the Alpha or the Aurora?
What kind of budget do you have?
I am not a fan of MMOs...
Then don't play them? I'm not sure what you're saying here.
...I don't think super graphics engine are necessary for playing a good game.
Depends on your point of view. And it depends on the kind of gaming you do. Not all games have a demanding graphics engine.
And would a Alpha be like buying a consoles? and can I update its hardware like a pc?
It's marketed that way, but has some upgrade options. Most notably the RAM & CPU. The GPU is designed to be upgradeable with the Alienware Graphics Amplifier, since it's very difficult to find a standard for the mobile GPU design.
would it over heat?
Assuming a cool room, out of sunlight, not in a confined space, and no dust buildup in the Alpha: no.