I think this one is mostly reflective of the risk/reward payoffs of aggressive and unusual play in any particular game. Play to win means - force the confrontation, take gambles, push your way into a surprise advantage. Play to not lose means - lean on your techniques, stay in control of the situation, build an advantage gradually.

And for most games, most of the time, playing to not lose is a more reliable way to win, because it is more consistently rewarding to practice, even though it can result in a boring risk-assessed playstyle. Playing to win is an emotionally-driven way to do things and good technique will usually counter it, but every once in a while, late in a match, the mask slips and there's an opportunity to make a play on an overwhelmed opponent.

Speaking specifically about fighting games, there are multiple levels of progression, and thus different mentalities. At the lower levels of competitive play your best options are in fact, "playing not to lose" and letting your opponent make mistakes, then punishing them. At higher levels, execution is assumed for 90% optimal combos and situations, and dropped combos are uncommon. In those situations you need to force your opponent to make mistakes that they wouldn't make normally, and thus you "play to win". I can make a similar analogy in tennis, where low-level matches have a low ratio of unforced errors to passing shots, whereas professionals have a higher ratio. Professionals in competitive fields are working on a different level where consistency is expected.