"Do you have other shoes?"
First of all, if I had only two options for marking I would say "yes, you're correct". And I think you should report it.
However I believe there is a reason to favor 他 over 別, so let me mention it here because it may help non-native Japanese learners.
他 is an almost equivalent Japanese word for "other, another" (essentialy it's "outside a certain domain"). By saying "他の靴はありますか" it can mean either "Do you have other shoes?" or "Do you have another (pair of) shoe(s)?".
Whereas, as Neamhain has mentioned, "別の" implies that you're thinking of another single (pair of) shoe(s). It is because the essential meaning of 別 is "different" and "別の靴はありますか" would sound like "Do you have a (pair of) shoe(s) different than this one(/pair)?".
c.f. 他人 and 別人.