There are no nutrients that only red meat provides, which is good because most people had little access to red meat on any kind of regular basis until the modern era. You might be thinking of vitamin B12, but that is found in a broad range of meats, or of rabbit starvation, but that refers to having very little fat at all, and fish, oils, etc. are a perfectly good substitute. The fact that the American Indians did pretty much just fine with zero access to red meat outside of game (and llamas and a few relatives in South America) kind of indicates that.
That also shows that having "mass extinctions" of people in Northern Europe is an obvious gross exaggeration, considering that nothing of the sort happened in the Americas. I seriously doubt that Europeans will somehow be more likely to die than people with only guinea pigs, turkeys, and llamas (and those not even everywhere) from nutritional shortages when, as you admit, they still have access to fish (with, I must remind you, significantly better boats and ships to collect seafood from than the American Indians possessed), poultry, rabbits, sheep, goats, and cows.