How is Rome equal to China when the latter still exists and the former died?
Which China? Han? Ming?
Plenty of groups claimed to be the successors to Rome (Constantinople, the Germans, the Ottomans, the Russians), but they didn't control the same geographical area; in some cases they didn't even overlap it. Those who claimed succession in China controlled China the geographical region, they weren't all direct successors to the previous regimes.
Because of the nature of the canal system that connected China when compared to the Mediterranean that connected Rome, it seems more likely that a single polity could control the whole thing. You don't need to invest in maintaining the Mediterranean to make use of it, you just need to maintain your own ports and your own shipyards. The canals have to be maintained against sediment, the locks have to be manned, they are so useful that they become an essential way to feed cities, and they can be sabotaged in times of war (far more effective than piracy at blocking trade). The economy of China breaks down when it is divided into independent polities, the economy of the Mediterranean doesn't.
Had North Africa remained Christian, I think it's likely that we could have seen a second flowering of Rome (or Constantinople-as-successor), one that again dominated most of the Mediterranean. Had Spain remained Muslim, and/or had the Ottomans conquered Italy, there is a chance they could have united the Mediterranean littoral, and there is a chance they would have called or considered themselves successors to Rome.