I don't know what CSGO is but the answer to the question of whether or not an application will overheat your CPU is an emphatic "no."
See this answer for additional reference.
Whether you run something in Terminal to max out your CPU (as in the linked answer) or a GUI app, both your MacBook Air (all computers for that matter - PCs and Macs alike) as well as the CPU itself has thermal protection mechanisms built in. The fans will spin up,
kernel_task will consume massive amounts of processor resources, the CPU will scale back and even shut itself down if necessary.
As for your game....
You didn't specify which CPU your MBA had nor how much memory. However, it's a pretty safe bet that your configuration as is just dosen't have the horsepower to drive the game. Your MBA won't suffer, just your gameplay experience.