'isn't related' tells us about what Basque 'is' or 'isn't'. 'doesn't relate' tells us about what it 'does' or 'doesn't do'. We more often talk about what a language 'is' (see the first sentence 'Basque is ...'). I would unhesitatingly say that 'isn't related' is the better answer, but, as Jack has explained, 'doesn't relate' is possible. To me, 'doesn't relate' is awkward here, but I can't explain why.
I would add that 'isn't related' here is not really a passive voice verb. Yes, it has the same form as a passive voice verb and it started as one, but it really is an adjective. We can test that by substituting an undoubted adjective like 'like': Basque isn't like any other language in the world.
Note that in terms of people, there is a big difference between 'Jack isn't related to his boss' and 'Jack doesn't relate to his boss'. In terms of languages, there probably isn't much difference.