Looks like a perfectly apt use of the word. A fatalistic worldview can mean, for example, that they expect humankind's destructive impulses will always lead to its own destruction.

As a non-native speaker: do you care to elaborate why you think this word is incorrect here?

The word refers to a belief fate or destiny; but the usage here implied negativity or pessimism of some kind.

A "pessimistic outlook" is probably closer to what they wanted to express.