Finally! I have Absolutist's Mahjong game registered (and it only took 13 days).
They sent me a different registration code, a different version of the name I'd given them(!), and the same download link again. Then they suggested I deinstall the version I had, download from the same link, and reinstall. Instead, I tried the new registration info with the game I already had installed, and it worked.
However, it's not the greatest Mahjong game I've ever seen. The music is choppy, and there are some blank tiles in the games. Sure, they match up with each other, but really! Other than that, I like the tile set(s?).
BTW, I kept replying to their emails, and the same person (Lilian) replied to each one. It took a while, but the most recent email acknowledges that there was a registration problem, with the Mahjong game, anyway. And, hearing what you all have experienced, I'm surprised that no one tried to put me off by asking for screenshots!