Unfortunately, In it's current state, I don't think that games such as Rust, H1Z1, and Skyrim would do very well on such a system. The upgraded CPU (Core 2 Quad) should be able to handle older titles such as GTA-San Andreas and games from that generation, but would struggle to push 30+ fps on anything newer, unless some overclocking can be achieved. Furthermore, the Nvidia Quadro NVS315 is several generations old and was not a high end card even when it was introduced. This combination makes games like Rust and H1Z1, which from what I know are pretty CPU bound and not the most optimized, rather unplayable.
Some tips to improve performance. Overclock the CPU if you can and try to get the RAM up to 8gb. If possible, for your own sanity, buy an SSD, even a small 64GB one is preferable to none, in order to at least install the OS on. If you are looking to game, then the largest single improvement that you could make on this platform is to find a low power, low profile GPU such as the Nvidia gt-1030 to replace the Quadro NVS-315. With these improvements, you are looking at a system that could play esports titles such as CS-GO, LoL, and DoTa 2, at reasonable frame rates and resolutions. However, don't expect to be able to play the latest and greatest games (At least not 30FPS+), even at sub 1080p resolution and lowest graphics settings.
Good luck on the starter and try to temper your expectations. Have fun with the build!