Translation:Do you play tennis at the old department store?
In this particular case, I think that "by" (which was rejected) is the correct translation. Playing "at" the department store implies that there are tennis courts there, which maybe the case in Hungary but not where I live. Of course, you may still play tennis in the aisles but not for very long.
You forget, we are talking about a country where kindergarten teachers fly above the trees and shout by telephones. Why wouldn't they play tennis at the old department stores too?
I also thought at the old department stores did not make sense. It should be by.