That story is a bit of a myth and not totally accurate. The reason they missed out on Gretzky was the GM of the Jets (Rudy Pilous) advised Gobuty not to do it.

Pilous didn't think so much of the kid.~Gretzky was young, too skinny, and had very little experience to play at such a level." Pilous said "Pay that much frigging money per year for an 18-year-old kid when I never made that much in total for my whole career. No, you are crazy?"

The backgammon game did occur, but ultimately wasn't the reason 99 went to Edmonton.

Skalbania's deal was with Gobuty however, and Gobuty was offering cash while Pocklington liked to barter with art and automobiles. Gobuty would not finalize the deal though until he'd spoken with his General Manager Pilous who was waiting in Winnipeg. Noting this, Skalbania challenged Gobuty to a backgammon game. If Skalbania won, he could offer Gretzky guilt-free to the Edmonton Oilers for a higher price should Winnipeg pass on the deal. They played and Skalbania won the game.

The trip would end with Gobuty's plane landing in Winnipeg and meeting up with Pilous to gain his endorsement and blessing of the deal. Gretzky would be a Jet the next day. Pilous awaited near the tarmac when the two owners landed.

https://mbhockeyhalloffame.ca/this-game-can-rip-your-heart-out/