This wording is backwards:
Which rewrites .com/game.php?game=34 to .com/arena/MW2. Its the other way around, the path /arena/mw2 is mapped to /game.php?game=mw2.
You don't need to do a thing. The rule you have will still match the MW3 as your rule specifies it must end in /arena/(.*) which it does. You only need to alter the pattern if you need to capture which platform it is on.