For other informations you can click on the word "svého". The translation is correct. You can use "their, his, my":
They are buying their horse. = (oni) Kupují svého koně.
He is buying his horse. = (on) Kupuje svého koně.
I am buying my horse. = (já) Kupuji svého koně.
that doesn't answer the question. I had the same issue. I wrote "their" but the correct answer was "our" which wasn't indicated in the tip. Does Svého refer to ownership of the subject?