Well if our robots beat your robots in killing each other, the logical next step is that the robots would kill the human opponents. So it’s not quite like a contrived chess game if the humans are reasonably inferior fighting machines.

It’s more like proxy battles, and in real life we do this with expendable humans rather than robots. When a side decides to surrender it’s not necessarily when the last person is wiped out... usually done when the military is near or close to defeat.

OP is suggesting that one day robots could outclass flesh and bone humans so much that real humans will be like the women and children of past society that will not have to fight in real battles.