I got it for free too, yesterday. It still works. And I also think it's for keeps.
I have no idea why the play button would be greyed out though. Except something must have changed since last time you used it. Maybe an update? (It happens). Have you tried re-installing the GOG client? Or the game?
Btw, can you start the game from the Start menu? (Start menu - All programs - GOG.com - Obduction - Obduction. At least that's how it appears in Windows 7). This just occured to me from another discussion thread here.
It might help if you provide some more info about your system (not neccessarily, but it can't hurt. Like Windows version, graphics card and driver version). Then maybe someone can get a better idea about what it might be.
EDIT:
There's also the "More..." button next to the Play button, with "Manage innstallation" (or similar). It has a "Verify / Repair" option, tried that? (Maybe a stupid question, just thought I'd ask anyway).
Post edited June 02, 2019 by coilwinder