Videos and Excerpts working at the same time?

Do you have the Page Header add-on set on your single posts by chance, or just the regular featured image?

Page header for posts above content.

Single post: http://telezjetele.cz/hirschberg/
Home page: http://telezjetele.cz

Can you try it with a regular featured image instead of using the featured image from URL plugin?: https://www.screencast.com/t/l7J9Hqhl6p

It does not make any difference, just tested.

Can you deactivate it and let me know so I can inspect the code?

Well It is a live site, deactivating means a lost of all featured images. Please inspect quickly :-)

Ah, I see the issue. This will be fixed in GPP 1.4 :)

Genius!