Just finished my first full game, but this can't be right?

Indeed, I own GC III for years, love it, but don't play often.

Still over time I had a number of games, but I often quit when I'm on the winning side.

So now I wanted to complete at least one, but as I thought I was winning, the game decided I lost.

Once I became the leading civ in almost everything I destroyed all but the one civ I was allied to.

But after I destroyed the last other, non-allied civ, leaving only me and my ally I thought this would give me an alliance victory (IIRC it worked like that in GC 2)? But to my surprise the game said "DEFEAT".

Why is that? Is there something I missed?