Yes, because in the original sentence there is 'a' which is an indefinite article, which is equal with the Hungarian "egy", that can be omitted. So "Az egy szék" would be another correct answer.
The answer to the item, "Yes, that is a chair" should be
Igen, ez egy szék, not the answer given, which is "Igen, az szék," which would be "Yes, that is the chair."