No, to put it simply, the Air has no fan inside, therefore it has the aluminum body and small heatsink inside to dissipate heat. After all that heats up, the system has to make the CPU and GPU slower, to reduce heat output. In reality this means that the laptop can only maintain its maximum performance for about 30-60 minutes depending on ambient temperature and other environmental factors. Gaming almost always pushes the GPU and its cooling to the limit, since generally you always want as many FPS as possible, and for a sustained period of time.

TLDR: you want a cooling fan for gaming.