I guess I see it as "I've won the game" when I reach a feeling of FI and don't need to work anymore. I'm not fully RE yet and of course it's all just numbers, estimates and projections, but there is an emotional component to reaching a goal number.
The feeling of freedom was my original goal with FI, and in life, and I have (more or less) reached it, so I supposed reaching a long-held goal feels something like winning. If I am understanding the question... But "game" is maybe the wrong term, because it seems too frivolous. It's more like - the rat race is over. The race is complete. There was a lot of striving to reach a goal, and now there isn't.
Beyond FI I don't see as a game at all. But I'm not doing the behaviours OP is talking about - I am not investing for fun. I'm also not a gamer, so who knows. People who are into gamification of everything might see investing as a game, but I just don't.
The interesting thing about this question to me is - people seem to be getting into investing now as if it's a game. It's great that investing has become accessible and more democratized and available to all, but I'm not sure the gamification of investing is really all that healthy or sustainable. There will be more and more apps that make it easy to buy single stocks, based on social media buzz rather than company fundamentals. Like the whole Gamestop thing, buying a stock just to mess up the hedge funds who've shorted it; or the aftermath of this - jumping into a stock as it's going up to try to catch some of the upswing without knowing anything about the company, etc. I'm going to sound really old here for a minute but - because my DH and I have talked about investing with people (in general terms) for many years, now a couple of our nieces and nephews (i.e. kids in their 20s) are asking him for investment advice. But they're not looking for the type of advice we have - buy etfs and hold them for a long time - they're looking for hot stock tips. What's the next Gamestop? What stock that's low right now can I jump into and watch it go up 1300%? That kind of thing. Umm.... Sorry kids, don't have an answer for you. I've read a lot of articles about this like it's a new trend, but to me it just seems like a new version of the get rich quick scheme. It's gambling. And it's all fun and games until you lose your life savings!