The sudden downfall in the chart looked so strange, I thought they must have conflated the city of Rome with the Roman Empire. But no, people actually left the city proper in droves, as resources became unavailable and the city fell into overall disrepair:

"The decline of the city's population was caused by the loss of grain shipments from North Africa, from 440 onward, and the unwillingness of the senatorial class to maintain donations to support a population that was too large for the resources available. Even so, strenuous efforts were made to maintain the monumental centre, the palatine, and the largest baths, which continued to function until the Gothic siege of 537. The large baths of Constantine on the Quirinale were even repaired in 443; and the extent of the damage exaggerated and dramatized (according to "Rome, An Urban History from Antiquity to the Present", Rabun Taylor, Katherine W. Rinne and Spiro Kostof, 2016 pp. 160–179). However, the city gave an appearance overall of shabbiness and decay because of the large abandoned areas due to population decline. Population declined to 500,000 by 452 and 100,000 by 500 AD (perhaps larger, though no certain figure can be known). After the Gothic siege of 537, population dropped to 30,000, but had risen to 90,000 by the papacy of Gregory the Great."

https://en.wikipedia.org/wiki/Rome#Monarchy,_republic,_empir...

When Charlemagne went to Rome for his coronation, only maybe 20000 inhabitants remained. To reach the Pope's dwellings, you had to ride for miles across the immense ruins of a former million-people city, a sight that stroke deeply the Franks.

You’re certainly misrepresenting something here.

The population of the world doesn’t follow this chart which simply implies Rome became irrelevant in history and people moved elsewhere.

I think that was their point

Their point was more akin to “all cities have been abandoned as civilisation ceased to exist”.

If that was the case we would observe a definite decline in population numbers across the world.

We don’t see that which either implies that the existence of civilisation wasn’t the prerequisite for our survival or that civilisation went elsewhere.

I am betting on the second one. By the time Rome become irrelevant we observe the raise of Paris and London.

Or the population dispersed into rural areas and returned to lives of subsistence farming.

Sure, but where? There wasn’t an equivalent of old Rome anywhere west of Constantinople.

Keep in mind that a graph of Constantinople would probably show a symmetrical climb around the same time

What a rebound. What happened to revive this city?

In 1870 It was annexed to the rest of Italy, the Pope lost his temporal power and it was made into the capital of the newly unified state. That meant moving all the administration and building a lot of new areas. That is on top of industrialization and a more general population boom.

The point is more how small it was just before that: a population of around 50k and much of the Roman ruins in the center used as a pasture.

Industrialization.