It's a temporal question. If you decide in the middle of a competition that you don't care any more and want to quit/forfeit/throw the match, then you broke. You committed to playing an event, presumably because you thought you could win or at least compete, and instead your mental stamina broke and you gave up.

IMO, it's less the intent that you have when you quit - the intent is almost always at that point that you don't want to be there any more doing the thing. The more important part is the intent that led up to the moment where you quit.

In some ways, it's similar to quitting any job. If you just have a bad day or week at work and put in your resignation with no other plan because you just can't stand coming in to work again, you "broke". If you're still working, but interviewing elsewhere, get another job, put in your notice and walk away with something else lined up, it's a bit different.