I think that would definitely have been the case in my game, their starting position was quite powerful. Giving an agricultural civ two grass-wheat tiles adjacent to their capital gave them +5 fpt without irrigating (which they didn't). They also built the Pyramids, had iron, horses and 3 luxuries in easy reach (on an otherwise resource-limited map), and only one border (luckily it was mine!). I can see if I hadn't taken them down in stages, they could have grown pretty powerful, and it sounds like your games are evidence of that.
BTW Regarding resources, I think it was stated this was a random map, so kudos to the RNG!
The scarcity of the resources (IMHO) is an improved feature of C3C, at least it drives more strategic decision-making. (Obviously this can backfire if the human gets all the resources, not much fun then). This worked out quite well, as each resource-tech was a moment of suspense. I also like it that not every AI develops along identical paths now, Rome didn't seem to have horses until late so they were playing an all-infantry variant! I also noticed that there was only one Incense on the entire map, so it's no longer automatic to get 8 luxes and forget about happiness.