Well, and "shop" and "mart". Still, even if we branch out to a few less obvious ones, we're looking at a few dozen possible names at most, and some of them are ridiculous like "The Software Application Emporium", and oh man hold on I have to run over to the trademark office real quick.
The term app was first used by Apple since at least the early 80's and even Mac OS X and iOS(and NeXTSTEP and OPENSTEP) use".app" as the extension for applications. Steve Jobs was using the term "app" long, long before it was popular.
There aren't really a lot of synonyms for a place where you buy things. Store and marketplace are the two obvious ones.