Should I build this gaming pc?

I found these gaming pc parts on this website
http://pcpartpicker.com/user/alanhenry/saved/1x6N

I feel like it kind of to cheap. So I was wondering if I should upgrade some parts or is it ok to run. Games like league of legends and minecraft. I'm using a laptop and when i play it is still slow with the graphics turned down.

Any suggesting. Or send me a build list range to $800.
The computer with cost $736 with monitor, mouse, and keyboard.

http://lifehacker.com/...0-and-1200

Sorry it hard to explain what i want to say.

Added (1). Or get this?

Added (2). Some stuff is sold out and i don't want to buy there wrong item. Can someone make me a list please and thank you

Added (3). I want to play other games too though.

LoL and Minecraft aren't exactly demanding-- yes that would run them fine. Minecraft would be like >100fps