I never like the term "won the game". It's not a game. It's life. If you lose a game you feel a little sad, angry, dejected. But if you run out of money you might be living in a cardboard box, or eating cat food. Or to a lesser level, spending your days at home because you can't afford to take a trip, can't afford to fix your car (if you still have one), and so on. Or maybe you're scouring the want ads to see who is paying better than minimum wage to an old-timer who doesn't have current marketable skills. None of this sounds like much of a game to me.
I suppose what you're looking for is when you can breathe and sleep more easily because you don't see any of the above happening except for a black swan event. For me that was sometime around when I retired, or maybe even during OMY times, or maybe a few years into retirement when my nest egg continued to rise even as I had no more work income coming in.
My other issue with the "game" mentality is that nobody knows the rules. I feel very secure nearly 10 years into retirement. But what if one of those black swan events does happen? Where is that in the rules? The only game life possibly compares to is baseball, where no matter how big of a lead you have, you can still lose if enough bad things happen. It's not over until the final out, which I guess equates to your death. Maybe beyond death if your needs went beyond you, perhaps to leave enough for a special needs child. You could be pushing up daisies but still "lose the game" if the trust for that child runs out.
Sorry for the rant. I think I'll just ignore threads that talk about "the game".