It's not the worst choice, but for over $500 I am not all that impressed with the 720p screen, and the AMD processor. Also, realize that this is integrated GPU so the gaming will be limited to more casual.
I really do not play many games nowadays so I don't know how well the A10-7400p and Radeon R6 (kaveri) can handle that game.
I realize that you are only a college student, and you probably do not have a large budget to work with, but I think you are better off buying the Asus laptop I recommend which is not much more than you were going to spend before you found the Asus you wanted on Newegg for less. The 1080p screen means you will have a larger desktop area which means you can have multiple windows open that could be helpful for your schoolwork. For example, if you are writing a paper and need to do research online, you can have the word processor program on left side of the screen and your web browser open on the right side of the screen instead of switching between programs.
Eventually, you are likely going to play a more demanding game than H1Z1. The nVidia 940m is not exactly considered a "gaming GPU", but it is a lot more powerful than the Radeon R6 (Kaveri) graphics core. The 940m should be fine for playing most games at 1600x900 with medium settings. The Asus I recommended can save you money in the long run because it is possible that sooner rather than later you will likely feel that the less powerful Asus is no longer good enough for your needs and you are looking around for a new laptop.
However, if money is a real concern, then get the less powerful Asus laptop from Newegg because it is a decent bang for the buck.