Why in this case we are not using an article before a profession?

Tanya, 

The lesson you linked covers the fact that an article is not used when describing someone’s profession - not using an article in this situation is basically the ‘default’ position. 

( To aid understanding, I have seen it described on some sites as the profession being used as a type of 'noun-adjective', when it stands alone in this context )

There are exceptions, also discussed in the lesson. However, this sentence does not include an adjective qualifying ‘ directeur ‘ - the prepositional phrase itself does not give rise to an exception. There is also a similar example in the lesson. 

The attached link to ‘ l’article zéro ‘ might help also. 

If there is something more specific about the sentence you are questioning, can you explain a bit further ?

https://kwiziq.learnfrenchwithalexa.com/my-languages/french/glossary/8