Perhaps you are launching from a desktop shortcut, rather than the Galaxy play game button?

If you launch the game from outside Galaxy, in any way (Adding the game in Steam and launching the game through it, launching directly from the executable, etc.), then it won't be able to track your play time and you won't get any achievements. So if you care about those things, always launch the game through Galaxy.

See what the others said and make sure you are connected to the internet while playing. From the GOG Galaxy support page:

PLAYTIME AND OTHER STATS AREN'T BEING SAVED
The stat tracking requires that you're connected to the Internet at the moment you exit the game. We will be improving this functionality, to make it more robust and less susceptible to temporary connection issues.

http://www.gog.com/support/support_view/bgog_galaxy_troubleshooting_and_useful_informationb#STATS_TRACKING

Thanks for replies. More often I use desktop shortcut but I have started it through Galaxy many times and it has no effect. I have there some achievements but the time is probably somehow bugged, so maybe i could try reinstalling Galaxy if it should normaly work.