Can I install games from the App Store on my PC?

A while back I bought Bioshock on the App Store and played it on my Macbook. This version was relatively cheaper than buying it from Steam and at the time I only had a Macbook so I considered it a win. However, recently I have decided to purchase a new PC to play games, I've decided from now on to buy games on Steam since that is the easiest way for me presently. I have no problem with the App Store or Apple products its just that I wanted use something else. I don't feel like wasting my money by buying Bioshock 1 again, a game I already own. I just want to know just in case I want to dust this game off for some good old times.

Is there anyway I can download my copy of Bioshock from the App Store to my PC?

(If worst does come to worst I can just wait for another Steam sale...)