It's interesting that no name of the author is found on the article. At a guess, I'd dare say the writer is actually Russian with a high level of English, and has just translated the expression literally. There are a few other minor errors and odd phrasing in the article and on the site which a native speaker wouldn't make, but a second-language speaker would. I think Ben has given the best natural English expression. We might also say "success has gone to his/her head".

Sorry Iris, I never heard any expression with 'stars' in the sentence, that you are looking for. I'm tiring my best to earn a 'Best Answer - Chosen by the Asker' from you. Maybe next time.

They are narcissistic. Which basically means to have a large ego. The world revolves around them.

I think we usually say "She has a big ego" or "She has an ego problem".

Thank you for your comment.Yes, that seemed strange to me that I could find only one article on the Internet where "star sickness" was used. Now I understand why.