https://www.youtube.com/watch?v=aj2o5xaJJoI I assume thats the one youre talking about? Imo I would try and get an intel chip over the cheap amd and a 750ti over the r7 360. but if they need it to be exactly $350 and dont want to do any research on parts and pricing then it would do the job. It could play cs perfectly fine and newer games at ok fps on medium-low. or even medium-high depending on the title.
EDIT: quick look at the i3 6100 and it seems like it would be better. although the price of the amd cpu in the video its hard to beat if youre poor.
also keep in mind that if they dont already have windows or they cant get it for free. that'll be $100 added to the cost of whatever they buy. i forgot about that when i planned my pc and had to ask my bro for some help