The "steam must be running" issue is pretty annoying... I have played the game a few times now, but that keeps popping up. So here is what i did to get it running... It will take some time, about 10 min but you can do stuff while it is loading. I havent found out wich one that helps i have just pretty much smashed my keyboard until something worked (Not really). First thing you can do is right click on the normal MW2 in steam and right click and press "Properties" on the bottom. Press "local files" between "language" and "updates". Press "verify integrity of game cache". If that doesnt work try "defragment" the one under.
Or you could start MW2 and close it down and try to start AIW. Try this in different orders over and over again and it might work... It did for me, but you have to do it over and over again to start it up the next time this error pops up. Damn annoying.