Not that I have ever heard. Like you, I have spoken British English from birth (well, not quite, but from as soon as I started talking!). "They have 8 seats free" is the usual way of expressing it.
The given translation is not normal English. We'd say, "They have eight seats free", not "They have eight seats open". (I put "free", and thankfully, it was accepted).
For the theatre we would certainly hear "...seats free" but for a restaurant or course we'd probably more often hear "...places free" which fits well with the German sentence. As for "...seats open" - definitely for those across the Pond ("Über den Teich", which probably doesn't make much sense in Germany).
since u can't have 8 squares, places open/free, in this case platz means seat, ...but in the vocabulary the translations for platz are indeed square, seat, piazza, place :) for instance...Das Jelačić Platz ist frei...as a sentence just doesn't make any sense (picture below) http://img156.imageshack.us/img156/4171/trg2000kl1.jpg
I am doing an exercise with tapping the word bank. It does not include "free". I tried "they have eight seats" which would cover most contexts in English. So I have lost a heart and will be forced to use a phrase I have never heard when I come to the correction at the end. I am becoming more and more annoyed by having trouble understanding the English used by Duo.