I don't quite have the answer yet, but here's some info that may help:
If you right-click on the "redeem" link within the Mac App Store and select "copy link", you get this:
https://buy.itunes.apple.com/WebObjects/MZFinance.woa/wa/redeemLandingPage?s=143444
Opening that link in a browser doesn't launch the Mac App Store, but it launches iTunes on the same page that the link you posted goes to. If you mash-up that link with the one you provided, you get:
https://buy.itunes.apple.com/WebObjects/MZFinance.woa/wa/freeProductCodeWizard?code=YOUR_PROMO_CODE
Which also seems to work. I'm guessing that means you can use that link to purchase Mac Apps from within iTunes, but you'd have to try it.
Now the last piece of the puzzle would be to open that link in the Mac App store instead of iTunes. You can launch the Mac App Store application easily enough using a URL like:
macappstore://itunes.apple.com/app/someappid
But I have a feeling that the App Store app has a much less developed set of deep-links than iTunes because most of the paths that work with iTunes seem to return an error if you use the macappstore:// scheme.
Hopefully I'm wrong though.