Further to the answers to ypur identical posts at
http://forums.pcpitstop.com/index.php?/topic/204423-problems-with-a-gaming-pc/
http://help.howproblemsolution.com/1224698/problems-with-a-gaming-pc
I would assume the computer you have is this one
http://www.amazon.co.uk/FX-8320-1600Mhz-Graphics-Preinstalled-Computer/dp/B00PQVJRES
From the description, it has onboard graphics only, Whilst fine for everyday use, this is not going to suffice to any degree for modern games such as dayz.
The good (ish) news is that you should be able to fit a grasphics vard. according to the spec, you have a 600w power supply unit which should support a reasonable card. However I would advise that you check this, as quality is often not the best in such prebuilts,and it would need suitable output on the 12v rails (cheap power supplies will often put a huge potential on the lower voltage rails, 3 or 5v, and use this to bump their spec).
If you are new to this, it would probably be easiest and best to take it to a good computer shop. I assume you are UK, in which I wouldnt touch PC World with a barge pole- their tech support is good only for laughing at. (No offence to anyone that works there, but the number of times I hear them advise badly outnumbers the good by too big a margin).
Ask around if anyone can recommend a shop, or better still knows enough about computers to check your psu and install a card for you- its fairly easy, but really you want to have someone to advise first time out.
as for fit for purpose- the gaming in the title means pretty much nothing. Generally it is used by anyone trying to sell something as a bit better than it is, although I agree that not having a dedicated graphics card si stretching it. However the seller did list the full spec, which I know is no use to a novice but does give them a minor defence. If you are not happy with it, contact the seller, explain that its not what you expected, and ask for a refund. If that doesnt get you anywhere, try the Consumner Contracts Regulation (formerly Distance Selling Laws) which may help. If that still fails, contact Amazon directly, as they like to know what their sellers are doing. I would reiterate though that in terms of fit for purpose, it would be hard to prove its not.