AKAIK (based on my observation etc...), a person loses when they can no longer colonise or produce a colony ship (i.e. no planets and no colony frig/cap left)
I'll have to watch the whole replay to be sure, but I don't believe he had any more colonizers, and we totalled all his planets and starbases. Both my ally and I had clairvoyance and we were checking all the spots on the map that we didn't control. We weren't being completely systematic about it though, so it IS possible he jumped it into a system we just checked while we were scouring.
I did watch a little of the replay, and something did just occur to me. When his partner first dropped, he didn't realize that his ally was going. After thirty minutes of "Dude, are you there?" it appeared that he still hadn't figured it out. It's possible that after 3 hours of receiving computer whispers and not getting a direct response to his questions that he STILL didn't figure out that his buddy quit and he had a computer ally.
In that case, I can't COMPLETELY blame him for not quitting. He did appear to be new after watching the replay. I'll have to ask him if I see him online. If he DID figure out that he was stuck with an AI in a clear losing position however,, then I have no desire to ever play with him again.