Should I buy this desktop computer?

That should cover about any game you want to play. Plus it is upgradable to a point. I think you should have no problem with it. Cod ghost needs 6 gb just to get started yours already has 8. And I wouldn't even think of getting a gaming pc with less then a terra. And this one has it, I see no reason it won't fly well

You realize that the graphics are part of the CPU and have motherboard ports only. There's no separate graphics card or ports. I have no idea how that will affect gaming speed.
You realize there's no mention of a CPU cooling fan and heatsink assembly. If not there, your CPU will last less than a minute. Might be there, might not.
It is written that there's no OS. You will buy that.

DO NOT buy this to game on, no discrete graphics, you'll be lucky if the games even load lol. Also, hard drive size doesn't matter, get a 120gb ssd and see your loading times cut by 80%. But a large "normal" hard drive is a good idea to store games on, but to give you an idea, the biggest game I've played was 22Gb's (Ghosts).

There's no graphics card, there's no operating system. This will not run most games. This will run some low end and online games but you need a dedicated graphics card and operating system.

Yes it does not say what cpu cooler it comes with but most likely it will have the OEM cooler the cpu comes with. Really this is a good base computer but not good enough for gaming.

Other answers have explained all the faults its not something you really want to buy.

It is good, the micro ATX Motherboard has a PCI Express gen2 x16 slot so you'll need to but a graphical card before you can play games on it (which is around $200 - AMD Radeon R9 270X) and you'll need a cooler because of the OEM processor