Can you download a Mac version of a Steam game you purchased using a retail key?

I added Modern Warfare 3 on Steam using a retail key. The game wouldn't download properly, as in when I clicked install it would instantly say it's finished downloading even though nothing was actually download. I contacted Steam support and went through various steps to try to resolve the issue which ultimately ended with them telling me that the retail version of the game isn't compatible with Mac. When I pointed out that the Steam Store page of the game says it is compatible they told me that it's not the same as the Steam Store version of the game, which I found confusing.

So my question is, is there a way to get this Steam Store version? Like if I go onto the game page it says it's purchased. I'm not even sure if I'm asking this question right to be honest as I don't know the difference between a game purchased on Steam with money and a game purchased using a retail key. The only solution they offered was to download it on Windows, which really isn't a solution.