I have no idea when it happens but suddenly during dialogues, they get skipped instantly and I can't read them anymore. I have to go to the menu and come back to "fix" it.

Is it a bug?

It might be related to jumping in and out of the game, e.g. to check a walkthrough or achievement guide.
I think it's a problem with the underlying game engine from Adventure Game Studio.
(The Steam version has similar problems when displaying the Steam overlay window)

A) Try hitting TAB to stop the skipping.
B) Avoid leaving the game other then quitting it entirely.
C) You can try to narrow it down, by leaving the game in different ways:
- Alt + Tab
- Alt + Esc
- Ctrl + Alt + Del
- Windows Key

Check if the skipping appears.

D) Try running the game in windowed mode and not in fullscreen