Hmm, what Windows version you're using? On 7 without codecs is playing fine here. The movie is just an AVI that can be found on \DATA\movie\ on the Xanadu Next installation directory.
Maybe the logs on C:\ProgramData\GOG.com\Galaxy\logs can give a clue (that's Galaxy cfg directory for me).

See if "Play Startup movie" is checked on your config screen.

Already contacted support and got a reply.

Tried everything they suggested, but it still won't play the intro, even though the start-up AVI, wnich is in the same folder, plays fine.

Strangely, on my Laptop (also win7 64) it works fine, so I just have to play it there.

I highly recommend the K-Lite codec pack. I had issues on an older machine with Win7 and Nihon Falcom games' cinematics not playing, and installing the pack solved it for me.

Good it worked, but these codec packs are not necessary. K-lite in special, I found it strange that it had some crypted content on the installer (I used like 5 years ago).