score:2
The map is fictional, based on an anachronistic mix of Roman territories and supposedly some trade routes.
The colouring of Armenia and Mesopotamia hints at Trajan's time. However, at this same time, Northwest Africa was under Roman control and it is not coloured. Northwest Africa was only not under Roman control before the 2nd century AD and during the Western's half's collapse (despite being briefly reacquired by the Eastern half during the Middle Ages). The map is therefore fictional as before the 2nd century AD Armenia was not under Roman control.
Other inconsistencies are Southern Hispania not coloured despite being conquered much before Northern Spain, the absence of Sardinia and Consirca (conquered during the war against Phoenicians, though it could have been a graphical oversight), and the absence of Northern Gallia.
The string going into Russia also does not match any real life fact, only loosely resembling a mix of the Amber Road, which went to the Baltics, not Russia, and the supposed Steppe Road, which connected China to Eastern Europe.
Upvote:2
About those branching lines, I see 3 possibilities
There were certainly land trade routes running between the Roman Empire and the far east. However, most depictions of "the Silk Road" show it running South of the Caspian Sea, with an occasional one wrapping over its north shore, whereas both of these lines run far North of it. What trade there was coming from the northeast (eastern Europe) appears to have been largely trading in locally-collected slaves.
There were some split/join in the route, somewhat like depicted in the map, but it was going both ways around the first the Aral Sea, then the Taklamakan Desert, just north of Tibet. Both are considerably south and east of the split on the map.
So if trade routes was the concept, its very representational, and nowhere near geographically accurate.
This one would make a bit more representational sense, as those lines are close-ish to the invasion routes taken into the empire by the Huns and Goths. The problem here is it doesn't make much sense in the context of that show, as all three seasons happened centuries before that period (the map says 100AD, but it should be more like 300).
So I think this theory is unlikely.
As suggested by multiple people (particularly justCal in the comments yesterday), another possibility is that this was just an artistic creation of graphic designers who had no real concern for history, but just wanted to depict Rome as a giant bloodspatter on a map. In this case, those lines are just meant to be rivulets of blood, not any serious geographical item.
This theory would make the most sense if that map were generated for the purposes of promoting Season 1, which has the sanguine title of "Commodus: Reign of Blood". Sadly, I've been unable to dig up any further contextual information on this map, so its tough to say.
Upvote:4
Assuming that the red area indicates the extent of the empire, we can look for a period that fits. To start with, it would appear to be dated before the reign of Claudius or during the final years of the Western Empire, as Britain is not colored.
Oddly, neither are Corsica nor Sardinia colored, and they were acquired by Rome during Republican days (Corsica at the end of the second Punic War and Sardinia a generation earlier).
So far, the map is either real early or real late. But real early can be ruled out by the extensive red in the East which Rome didn't pick up until centuries after those those islands.
And those two lines trailing off into Siberia belong to no era of the Roman Empire at all! (Nor do they match any silk roads that actually existed -- not that Rome ever controlled more than the western ends of any real Silk Road, anyway.)
As the OP noted, the state of Africa is hard to fit into any era.
Finally, the map seems to give Rome some unlikely possessions in the Middle East.
So, the days of the Western Empire are ruled out. What about the Eastern Empire, say under Justinian? That, too, is ruled out by the extensive holdings in Gaul.
The map appears to be partly imaginary or rather careless. (I'm betting on the latter...)