I figured there had to be another way, and eventually found that the mdls command gives some of this information. Running mdls <app name> returns a lot of information, but near the top of the list are a few lines like this:
$ mdls /Applications/Smarts.app kMDItemAlternateNames = ( "Smarts.app" ) kMDItemAppStoreAdamID = "438671026" kMDItemAppStoreCategory = "Music" kMDItemAppStoreCategoryType = "public.app-category.music" kMDItemAppStoreHasReceipt = 1 kMDItemAppStoreInstallerVersionID = "8330689" kMDItemAppStoreIsAppleSigned = 1 kMDItemAppStorePurchaseDate = 2012-06-13 07:14:43 +0000 kMDItemAppStoreReceiptType = "ProductionReceipt"
The kMDItemAppStoreHasReceipt is what says whether or not it is a Mac App Store application, but you can see some other Mac App Store information there, such as the category (non-MAS apps have this too, interestingly), the purchase date, the application's ID, etc.
My interest in this is purely academic, but it could be useful to find all Mac App Store applications on a given Mac; you could use the kMDItemAppStoreHasReceipt key in a search, for example. If you run this in Terminal, you'll get a list of all your Mac App Store applications:
mdfind "kMDItemAppStoreHasReceipt=1"
Note that if you have any volumes excluded from Spotlight searches, their Mac App Store apps won't be listed in the results. (H/t to Thomas for that command.)
If anyone has any other ways of finding this information, feel free to post them in the comments.

