Our psychological health should be unconditional. It shouldn't be dependent on our experiences with wins and losses. Losing, which happens more often than winning and can have a direct connection with low self-esteem, is an inherent part of competition. So why do we let it affect our self-esteem if it is actually more common than we realize?
But the bigger question to ask is this: is there reason to think that competition is always psychologically damaging to some degree?
If losing has the possibility of dragging us down, does winning have the possibility of uplifting us beyond what should feel good? The rush of winning can lift us beyond our normal level of high self-esteem, almost to the point of looking down on our rivals. There's nothing wrong with winning or enjoying it, but it stands to reason that it has the same potential that losing does to affect our psychological health.
No matter the situation or the outcome, our psyche should have little to no connection to the result or outcome of a competition. It's okay to like winning, and it's okay to be a little down when you lose. But put it in context of these discussions to make sure you still are okay with yourself!