When I signed up for the gog.com beta I was promised a free game. I haven't found any way to get this and the support won't answer my mail. So I wonder if anyone else have been able to downboad a free game? An then; HOW?
Or is the whole thinsg just som bullsh***?!?

No it isn't, but it depends on when you signed up... because if I remember correctly the free game offer was valid until the end of September (at least the early access offer anyway). To get the free game, you had to buy one first.
All of this was explained in the activation emails and should be somewhere on the site as well.
If there is a new promotion for the current open access beta, I don't know about it.

Now, I understand you feel wronged here at the momment, but I'd suggest you should do a bit of research before sounding off in future. A simple search on the forums would have shown you that plenty of people have had the free game when it was available, and there were a few disussions about the closing date. Making it quite obvious you have missed the deadline.
And by the way, if you worded your request to the support desk as you have your post, I wouldn't expect an answer at all.

The details of the promotion are clearly outlined here. As noted, you've missed the deadline.