Ugh. That chart. That chart is awful. Potentially interesting information made entirely useless because of scale. Anyway.

Yes, the numbers are basically accurate, although plausible estimates for Roman Rome tend to vary between 500,000 to 1.5 million. The numbers for the Medieval city are probably rather more accurate--while I can't speak for Rome specifically, many Medieval era documents relating to census and other civic information survive: they are flawed sources because Medieval polities lacked the capability and inclination to do truly thorough demographic counts, but they are better than anything we have from ancient Rome. So what explains the disparity?

Primarily, because ancient Rome's population was "artificial" and entirely dependent on its relation to the Empire. There were a large number of ways in which the Empire itself served the city of Rome: the guarantee of grain shipments is the most famous, but also the importation of population via slavery, and the economic benefits of imperialism in the form of imperial largesses, the concentration of wealth, etc. These conditions which prevailed during the ancient period up to 400 or so (granted, in a diminished form by that point) but were rapidly lost in the next century. The big reason was the conquest of North Africa by the vandals: no longer could the emperors extract grain from there by fiat. The two sackings of the city in 410 and 455 more or less proved that the city was no longer a major concern of the emperors, who were now centered in Ravenna but in practice had a mobile court. This must have had an enormous psychological effect on the inhabitants: to give a modern example, recall the way people did not feel "safe" in NYC after 9/11 and moved away. The next century was even worse in many ways for Rome and for Italy, as Justinian's invasions starting in 535 set off decades of brutal warfare in the countryside. By the time Charlemagne entered in 774, the city was, in many respects, entirely unrecognizable. And as you guess, until the 1800s it was essentially a city of ruins, absolutely dominated by its ancient extent.

Making a direct comparison to modern cities is rather difficult, because industrialization and speedy transport has utterly transformed the way cities operate. It is rather impossible to get a straight comparison between what a modern and premodern city would be like: there is nothing like the latter around anymore.

A good source for Rome's collapse is Bryan Ward-Perkins Fall of Rome and End of Civilization.