Your PSU has enough power, what is ur voltage on the 12 rail? Slim chances that its ur PSU in terms of it not being powerfull enough, especially if its new.
It could however be faulty, if ur experiencing random shut downs, especially when using much power (playing games), then it makes sence for it to be ur PSU, and since there is little chance its not good enough, it makes sence that its broken of faulty and in wich case u should return it and get a new one.
Im sure u did some research before buying each part for ur PC, and since i dont know much abt PSU brands ill assume that its a good one and that the PSU isnt acting up because its cheap, even though a cheap PSU should still take a while to brake down.
Any part of u PC however could be triggering this, but if a component such as the CPU, RAM or graphics card would be having a hard time (because of a fan dying out for instence), then u would see a more violent power down, and u would probably smell smoke.
You will have to check to know for sure however if ur parts are doing OK. Download a program called Everest and evaluate ur PC. Google it.
Last but not least, and it would make more sence then a PC hardware component malfunctioning (because we are talking of an instant power down), Windows could be the culprit.
If u have a virus for instence, this could very much happen just like u have described.
However, it would not make much sence having a virus so early on, and of course u say that it happens more when the system is being used, like in a game wich dosent overlap in this case.
Try Everest and check for temperatures. But i would suggest to take the PSU back as soon as possible because every power down damages ur new hardware!
