I have not read that book, but I agree, we are not too much like Rome, though there are a few similarities. Not enough though. If we are still a major power 800 years from now, those differences may not be quite as far apart. Given the probability that we might be in end times now, one might be tempted to call this possibility as a long shot. Hard to say.
Rome also conquered most of western civilization. We acquired “proxy” countries. So did the Soviets. Much of that is gone now, and that only took 50 years to form and dissipate. China seems to be better positioned the we do for the future… for the moment anyway. They have their own unique problems they have to deal with. We will see.
Things move so quickly now, there might not ever be another “Rome.” That would be my guess. Right now, I think it would be impossible to predict the possibility of any sort of 1000 year empire / superpower happening anytime soon.