As you said you got the game off your other account.
Galaxy checks the account you're currently using and doesn't see the game as owned.
This is why you're getting that message.

However the game will still launch if you try to launch it.
It's just that stuff like achievements (if it has some) won't be awarded.

Edit: You don't even have to launch the game from Galaxy, just go to the folder where the game was installed and launch the game right there.

That's the thing. I really want to get achievements to earn points to get the first free game, Spelunky. Is there any way that I can connect it with gog?

Ok. I was talking to a friend about this earlier and he said that achievements would do it but apparently not. Thank you very much.

The sale FAQ is near the bottom of this page.
Unfortunately for you, if you hadn't already been doing the daily check-ins since early in the sale, you're outta luck if you were hoping to get Spelunky without spending anything. But you've got just over one day left to take advantage of the deals, and if you get the five badges that are still possible for you to get, you'd only need to buy one or more items totaling about $1.30 U.S. to unlock Spelunky. =)

No, he isn't. What am I supposed to do with my code?

Ah, how foolish of me! I forgot what forum I was in for a second.
(That means it's time for me to go to bed, I think. :P )