if he only has $200 he should just save it nothing worth buying for $200. The xbox 360 is dated and they will probably stop making games for it soon so in my opinion its a waste.
Well technically speaking, you could game on a netbook. Just install an Nes Emulator, and Mario bros, but for any modern games, no way. Don't go cheap on the Power, the HDD, I guess if you want slow read/write times.For a cheap gaming experience, you could check out AMD's APU's, but no way you are going to game that cheap. Save it, and get some better stuff.
if you have a computer to upgrade, it might work. i had an old hp tower that i was running games on. gave it to a relative that wanted to get into pc gaming. it had a c2d, 2gb of ddr2, a couple old hdds i had spare and a 5670 i upgraded from. it ran games, not well but good enough to get by. i never tested bf4 or metro on it but it worked for everything i tried. bf3, crysis 3 (took a long time to load) and a few other random titles. i wouldn't suggest that build but it was cheap. you can save money sometimes if you are careful on craigslist or ebay. even scavenging old parts can help, hdds, fans, case or a psu if they're decent. it all helps my friend. if you are talking all new, it would be hard to do and make something respectful.
It strongly depends on what games he'll be playing. To play anything fairly modern, Logan's $350 build is really about as low as you can go.
There's a difference between being able to simply "run" any game and being able to actually "play" such games at an enjoyable frame rate (anything over 30-40fps).
I agree with the others. Don't bother buying a 360 at this point. It's so old, it just doesn't make sense. Tell him to save up another $150 or so and build a proper entry level gaming PC.
How about a used Dell or HP small form factor computer. They are $100-$200 and have a dual core Intel chip. That includes a Windows license. You could only play old games but there are so many good ones.
I'm not saying this is better than building one for $350. Just throwing out the option.
I don't think a form factor pc is a good option for him. He is looking for something to game on, but it's gonna be darned hard to game at that budget, unless you get a bunch of stuff used for really cheap, or already have a bunch of parts. You could always sell some old stuff you don't need. I got $160 out of my old PS3 and some games on Craigslist.