I appreciate your honesty. Thank you.
From my perspective, 60% of our company are women. If, in an all-hands quarterly business review, I quoted The Game, I can tell you it would undermine my ability to lead the company almost immediately.
Regardless of the lessons learned in The Game (I'm sure you're right, that there are healthy lessons to be gleaned), one thing it focuses on (as you mentioned) is the focus on self.
I would argue that the lesson with a higher impact is to learn how to intuitively focus on others. If you're a solo entrepreneur hammering away at home, The Game is fine. But if you're trying to build a diverse, scalable culture, this book might be a disaster.
One book on teams that had a huge impact on me was "On Teams" (it's a collection of HBR essays).