It's not the same thing. The outcome of war is "who gets to impose their will", which is something that can change without any physical change. We could declare tomorrow that there's a new king of the world and if everyone accepts that, nothing actually needs to change. Producing food is not like that.
The point is eventually all that matters is algorithms. If everything is automated, if a lot of war is cyber war etc, you know already that the best algorithms applied to physical stuff will win, so why not just pit them against each other virtually?
As for the argument of "why wouldn't they just go at it in the physical world next", well they could, but after 10 or 20 wars where you see the outcome is going to be aligned to the algorithmic winner anyway you see there's no point other than to kill your own population.
For what it's worth I don't think this happens in 10 or even 100 years - it's stretching it to a much longer timespan.