Bruce Lee had more of a show than practical Martial Arts. He knew this, and played with it. He got challenged a lot. I still believe that is what eventually killed him, even though others say it was drugs.
The "fighting without fighting" is a form of "winning without fighting" and is a type of Martial Arts where you put on a show with a fictional enemy, win over that enemy and thus gets to loot and hurt those who believe you actually fought and won.
"Winning by scaring", "Winning without actually winning".
We see this a lot in global politics. It works because the show is indistinguishable from the truth.
It was in a movie, so the context was inherently a little contrived, but I think he was saying more than that by it. Yes, he was definitely a showman, but I think there was also a duality beyond that and that he believed in more altruistic truths and ways of relating to others beyond his performance. If you haven't seen some of the interviews with him, I'd recommend checking them out. He of course plays the cool cat, which was part of his MO, but there's more than that there. I think he saw some of the discrepancies though, and this is likely what lead to his more philosophical outlooks on some things.
I think in some ways he was still very much a young man, trying to make his mark and prove himself to the world. It would have been interesting to see the sort of person he would have matured into later in life.
