I know with other apps you can share them with a limited number of other Macs (if the other Mac owner authorises), so is it the same with Call of Duty 4?
Yes, but stuff on the MAS can be installed on far more than 2 machines. If you are only using a single machine it may not be worth it, but if you have many Macs, it's a far better deal. (Besides no discs to mess with, license keys to look up, etc.)