It depends on how you define "success." By your definition, it necessitates seeing someone else fail in order to feel successful. But I think that's a narrow view of it, and fewer things are zero-sum than people often assume (though plenty of things still are, yes).
A few examples come to mind. One is the craft beer scene. Microbreweries often adopt a collaborative business model with other breweries in their area, rather than being cutthroat and trying to run each other out of town. When a town becomes known for having a thriving beer scene, it attracts more customers in total, to the benefit of all the breweries there. It widens the proverbial pie. Thus, by association with that scene, all the individual businesses become more successful than they would have been otherwise. And in that case I'd say success is about more than money - name and quality recognition, and building a dedicated fan base would probably factor into it as well.
Of course there are limits to that model, such as a local market becoming too saturated, but I think it's a good example of success being a more nebulous term than only being dependent on defeating others.
