So, I have bought a documentary about Double Fine studios but from GOG Galaxy I can't watch it and from the web browser I can only download the files of the movie.

Why can't I stream it?

GOG disable it temporary... long ago... And still advertise it in many pages

Actually, in recent-ish versions of Firefox, you can...as long as GOG didn't package the download as a .zip file (which they usually only do for "bonus goodies"). But for any standalone movies (and even though it's classified as a game in GOG's catalogue, I would think Double Fine Adventure would count as such), you should just be able to click the download link and it will instead start to play it in the browser.
But, yeah, this behavior is enabled by the browser, not by GOG.

The solution from this post still works for me:
https://www.gog.com/forum/general/movie_streaming_gone/post7

When you go to download a movie, copy the link to the file, for example:
https://www.gog.com/downloads/the_art_of_playing/en1video1
And then change the word 'downloads' to 'video'
https://www.gog.com/video/the_art_of_playing/en1video1
And you should be able to stream your movie, this should work for any movie.