He may "insist" on alienware, but it's by no means the best option, as alienware doesn't make the computers they used to make. If you are on a budget, and building the computer from scratch is an option, I'd go with that, but assuming you don't know much about how the computers build look for these specifications.
My first point: Stay away from AMD products when it comes to gaming. Games nowadays have much better support for Nvidia graphics cards than they do AMD. However you do not need the top of the line card to run games. I ran with a GTX 210 for several years, and had no problems.
Intel I3, or I5 series: This is mostly dependent on your budget, If you were to get him something with an I5 processor it would probably run you a bit more money. I'd say for a 13 year old a good place to start him out would be a low end I3, I used something worse all the way up until last year and could still run games.
It's also important to make sure you know what chipset this is if building the computer. For Example my I7 processor is in the LGA 1155 chipset, so I had to buy a motherboard in the same chipset. This is what shows they are compatible.
When it comes to graphics cards it's all about your price point, and the monitor size. The smaller the monitor he has the cheaper a card you need, because it will have a smaller max resolution which I'm assuming he uses.
Here is a good guide to graphics cards
http://www.tomshardware.com/reviews/graphics-beginners,1288.html
http://www.overclock.net/t/1172764/the-noobs-guide-to-nvidia-gpus
Small Guide to what a computer has in it.
http://compreviews.about.com/od/PC-Gaming/a/Beginners-Guide-To-PC-Gaming.htm