80 000 000 people in Europe was in the begining of the 14th century but the population was at it's peak. With the soil having very good yeild for the era. Things then started to change because the climate got colder and it's population started to dwindle. So actually, 80 millions was too high for Europe.
The population of Norway probably topped around 200 000 people at the time for 150 000 square miles. Wich seems to fit the north and tundra thing. Sweden is more populated but it's climate is probably too hot to be a good example.
So you would end up with something like 300 000 or 400 000 people for the area and not 3 300 000. The density is in fact around 1.
By chilly mountains I think something like the Ural or the Alps if you want a more frendly surrounding climate. It would be around 600 000 for 16 000 square miles if you take Switzerland as example. 10 millions or so. Density 37,5 wich seems pretty high but not all the country is covered by mountains. If you want just mountains, Tajikistan is another example but the numbers are hard to find.
Lush highland: Like Ireland 33 000 square miles with 1.3 millions people or so. 11 millions (density 39)
Enchanted Magical Growth Forest (120 density) @ 310,000 sq miles. I'm not sure this make sense since it's mostly covered by forest wich are usually unsettled by humans. The population should much lower than that unless there is a magical explanation. Now it's 3 times the density of Switzerland wich was already high. The density should be around 5 or 10 maybe. Maybe around 2 millions
Plains & Massive Grasslands & Fields aka Russia or Ukraine. Or the Grand Duchy of Lithuania to nbe more precise. It had a population of 0,7 millions for 135 000 square miles. density 5. It seems a little low but it depend of the climate. 1,6 millions
Desert region, but with an enormous and thriving oasis and set of islands. Apparently Egypt had about 3 millions people at the time for 387 000 square miles wich give a density of 8. It make about 4 millions.
Jungle: the density is even lower than the forest since there is no humans cities but only villages scatered. The desity should be around 1 or 2 I think. Roughly 400 000 people.
Lava-like region. That's not an earth-like climate so I guess it's possible. 6 millions
So to sum up: it's something like 35,3 millions people. It's not exact but your problem is that some zone are too densely populated mountains, jungle and forest have a very small density as it's generally unsettled. And as for the plains, it depend of the climate so it might be higher. In general, the drier and colder the climate, the lower the density will be.
I hope that I have been able to help you figure out the numbers.
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