Backgammon likely wouldn't work for online play due to cheating. AFAIK Gambit used to have a Bitcoin option but they cancelled it because of that very reason.
I have been interested in Backgammon, though. Perhaps you could open up a thread in Off-topic and talk about some theory. I've been told it's the poker of board games. [Self-modded of course to avoid spam]
Hey... you created a chess thread before! Thought I recognized the style of writing. Good to see you again.
No. Gambit cancelled for other reason. They were scared about potential law problems. You can avoid cheating without ID verification using AI.
You must play 10 games without cheating and provide your mobile phone number. We all know not everyone wants to disclose their telephone data so you must make tables for both verified and unverified accounts. It should be fully transparent. After that, these games will be scanned using AI engine. And of course, you must also scan every real money game for possible cheating. If yes, then operator will verify that you weren't cheating before allowing to play for real money again.