In your sentence, "directors" = директоров is animate accusative masculine plural, not genitive. It is the direct object of ты видел and requires animate accusative case, which is the same as genitive for plural masculine nouns.
"Objects" of где are nominative case. Such "objects" (in quotes because they aren't a real object) are a kind of passive-voice subject of the question - flip it around and you get "The directors are where?
So, it's just an irregular nominative plural. Nothing else makes sense.
In any case for professions you can use the masculine gender.
1. А где директор? - this sentence fits for any gender.
2. А где директриса? - this sentence fits only for a woman, you can also use it, but using the first sentence is the best practice.
This excercise is currently multiple choice and marks the correct answer as wrong! Something is broken
I learnt two knew things about Duolingo today. 1 You can switch to typing on the keyboard from multiple choice. 2 Very occasionally it checks you punctuation. So I could do this exercise by combining these two!
In full flow the speaker sounds like the character "Quagmire" gigigty
Based on paragraph c) on this site I've found randomly on the web, both директора and директоры is used, without difference in their meaning. Anyone (native or non-native) care to comment on this? It would seem, even if 'директоры' wasn't wrong, it’s still not so popular to use.