The culture triumphs because it is a technological super power. It is a technological super power because the minds (the super AIs running everything) are given free reign (and presumably most of its industrial base is used to create more minds, and develop more industry).

I've always gotten the impression that the resources dedicated to maintaining and serving the humans in the culture empire are dwaft by the resources invested into developing their science and AI.

(I mean basically they have Von Neumann machines controlling whole star systems, obviously this level of industry beats most biological enemies)

It's worth noting though that there are several other cultures/species that are more advanced than the culture though. E.g., the ascended species that stewards the tomb worlds (and is in essence like a god compared to the culture). There are many other examples.

I don't think it was ever claimed that the culture was predestined to be the strongest, or anything like that.