I'm happy I can get all those game (time to finish Operation Flashpoint!). but I signed up when I was still running Windows but now I dual boot.
so, I was thinking, is it possible to get the game I bought here to work under Linux with Cedega or Wine?
Or is there some sort of special thing?

You should have reasonably good luck getting older games to work with Wine or DOSBox (also available for Linux), but I don't think it's something that gog officially supports. Would be nice if they did, though.

Me, I signed up to see what they had planned in titles and found out I could buy Freespace 2 so that I can finally PLAY it on Linux using the Freespace Source Code Project version of the engine against the assets. Dual booting sucks. It's a disjoint experience.
You can always try. I didn't look at the stated support of Direct3D which would be the likely snag there.

Since GoG is porting these games over to more modern Windows support, it is unlikely that DOSBox will provide you any use with the games available here. WINE/Crossover Games/Cedega's your only choice where there's not an engine port available (See: Freespace 2...).

the dos games use DOSBox. no special hidden magic there.
I had problems with the gog launchers with wine though. The installer worked fine.