Since Theresa woke this thread up... That's a clever suggestion, but doesn't quite work. Suppose even you put quotation marks around מסעדתי and המסעדה שלי; What's the role of זאת? If it should parallel the "it" in "Is it 'horse' or 'mare'", in Hebrew we'd probably use זה, definitely not זאת.
This sentence is fun if you enjoy the challenge of figuring out how “Is this my restaurant or my restaurant?” could possibly make sense. Actually, it only makes sense in Hebrew. For the English to make sense, Duolingo should have put quotation marks around both occurrences of “my restaurant”.
I like this example. Is it "מסעדתי" or "סכדה שלי"? Not unnatural nor bullying at all...