Is this possible to make?

I've been on a mobile gaming binge lately and was coming up with ideas for how I could make a gaming desktop mobile. So I looked around and found this little doohickey.

http://www.ibuypower.com/Product/Hexa

I was wondering if I could use either this, or an Intel NUC, and modify it into a portable gaming PC. I understand I'd need an external battery, a display, and controls for said gaming (and possibly more) but I was just curious as to if it was possible, and if it is, maybe someone could give me advice? I'm willing to put the work into it, I would just like to know if it's worth it.

Wouldn't it be easier to just buy a gaming laptop?

http://www.newegg.com/Product/Product.aspx?Item=N82E16856164013

There's the same exact thing with a Gigabyte branding. Tells me all I need to know; These things overheat BAD. They have too much power and not enough airflow. They will throttle down due to heat and that seriously negates having that level of hardware inside.

Would it be possible to take out the innards, and make a handheld 7 inch case with more airflow?