There is no winner take all in an ecosystem. If it happens, that ecosystem collapses !!
It is strange that you use this as an example yet fail to understand it fully.
Nature is a complex system ... with adaptive feedback. Every process is a cycle - has feedbacks that amplifies/regulates it. Yes there are apex predators, but there is no winner take all in an ecosystem. Living beings coexist.
It's a race with winners and losers because ego and money. Ego because … well, ego.
Money because whoever develops the most powerful AI and gets enough people to buy into it, will probably retain the top spot for quite a while because inertia (sort of like how Google got to be where it is).
I'm sure some level of paranoia feeds into it at some level. Whoever gets locked in the public's mindset will rule the world and if it's not a Silicon Valley magnate, then they are losers.