Should I be concerned that the fan on my 11 inch Air makes a lot of noise when I play Call of Duty Black Ops? It's a Mid 2012 version (full spec here).  I play the game with the lowest graphics setting possible (with Shader Warming turned off, texture quality set to low etc.). The game runs smoothly. The fan spins quite loudly and the machine gets hotter while I play, even for a short duration. Should I be worried that playing the game for a long time would do some physical damage to the processor core and/or do some other harm to the hardwire?
No, it will shut itself down in the fairly unlikely event that it gets hot enough to risk causing damage. It's designed to run hot with the fan at high speed when it's under high CPU load.