Wonderful metaphor in this thread about the chess game. (And I liked the amber lights one too.)
With the disclaimer of speaking for myself (not all Fi users): I do sense the game, that there's always a game; one that's in continual play and changing all the time. I have felt it since I was very young and it makes me sad sometimes, and sometimes angry, but mostly I find it unsettling. Why unsettling? First, because it does seem like a "game" - it's a game about power and who has it, who doesn't, how to maximize one's advantage, and minimize the risk of failure. Second, like most games, there are winners and losers. And third, there's always a sense of the "tally" - you can feel the people in your life who keep score on you. I know who they are. I know what I have to do to keep myself in the "black".
Fi-users may take longer to learn how the "game" works, but most figure out the rules as one goes along in life and realize that one must play too in order to successfully accomplish personal goals. However, when one does play the game (and I should add here, either the Te OR Fe game) it feels false, fake, phony; it feels like a game because it's not about who the Fi-user is, it's about using a system to the utmost advantage; myself, sometimes when I feel inwardly frustrated I think, "Why do I have to play this game in order to get accomplished what needs to get done here?" Do Fe-users get tired of having to play it too?
Now, myself, I am coming to realize I live a giant conundrum as an Fi-user who is an (enneagram) so-dom. The group is important to me, and I have watched how people interact with each other my whole life to try to learn all the "rules". I cannot even articulate this quite the way I want to so I apologize for that. But following all the Fe rules is very exhausting for me, but I have to in order to fulfill my personal value system of being a good person who cares about others. I am not sure how to reconcile all that.
For some inexplicable reason, sometimes I just feel a need to be understood in this area, and receive some acknowledgement that I do bring value to the table.