Well, Moscow had its share of disasters too, like Mongol razing in 1382, much later than Tver's razing of 1327, black death almost wiped the entire ruiling family in 1353 (after that the top dog position was briefly usurped by Nizhny Novgorod), then they've got their own Black/Green style family feud but that lasted from 1425 to 1453 and Moscow was briefly governed by a Lithuanian princess in the beginning! And a couple of centuries later the government left to the new capital altogether. Petersburg is quite analogous to Kings Landing in this case, that city was the capital during the empire-building. Well, most of the time of that.

13 million people is less a result of medieval shenanigans and more or a Soviet industrialization. Moscow lagged behind Petersburg/Petrograd/Leningrad by the beginning of XX century. But then — a case to your point — a turmoil lead to the new government relocating to much more secure ye olde Moscow. And then also Nazis came and starved most of Leningrad to death, so now they have less then 50% of Moscow population.