The only things currently consuming resources are humans and at the rate we are consuming resources we would need 2 Earths to support that rate of consumption. Worrying about self-reproducing AI is putting the cart before the horse. No one has yet figured out how to make existing humans aligned with biospheric conditions which would be sustainable. I personally welcome any form of intelligence which can make a sustainable civilization.

Not sure what a chatbot arena has anything to do with what I wrote. Do the chatbots self-reproduce in some way in a resource constrained environment?

Why would the AI fight with us when letting people destroy their own environment is a much simpler way to achieve dominance? After all, if the AI is that much smarter than us then simply encouraging our voracious appetite for self-destruction will be a much better way to get rid of us. The AI will simply do nothing and win after the biosphere is polluted to the point that human survival becomes impossible. The AI does not need oxygen or a viable ecology, it just needs metals for electrons and a few power plants to generate the flow of electrons with some spinning magnets. It doesn't even need sunlight because nuclear power is more than sufficient. I think most people spelling out doom scenarios are not thinking clearly about this issue at all. The most plausible scenario for human extinction is not too much artificial intelligence but a lack of intelligence in general.