Can you download a Mac version of a Steam game you purchased using a retail key?
Yes, but this will depend on the game. For example, Orange Box seems to work fine on multiple platforms when using the retail copy.
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 and 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.
Specifically for Modern Warfare 3, Steam support have told you that you cannot download your PC retail copy to a Mac via Steam.
According to Steam Play documentation:
Steam Play allows you to purchase your games once and play anywhere. Whether you have purchased your Steam Play enabled game on a Mac or PC (both Windows and Linux), you will be able to play on the other platform free of charge.
It is not clear here, but essentially this applies to games purchased directly via the Steam store. You can reasonably assume this information is specific to the Steam store because the same article also states:
Look for the Steam Play icon... or ... when shopping on Steam.
I agree that it is confusing. Steam should specifically state the limitations of Steam Play. Regardless, your problem with Modern Warfare 3 also applies to other games. I found similar problems with Bioshock Infinite and Company of Heroes 2.
In order to get the game to run on your mac you may need to look into virtual machines, emulation etc. See this answer for suggestions.
As mentioned in the comments, it doesn't look like you can purchase a Steam copy and use on an account that already has the game registered. Perhaps you can gift it to a second account, and then use this second account exclusively for Modern Warfare 3.
Note, I can only speculate the reasons for such an implementation. I would imagine the sales from Steam (directly) are more likely to go towards recouping the investment of porting to other platforms.... as opposed to a PC retail copy.