The point is these areas are still pretty actively Tibetan today, not just historically.

Is there a contiguous region stretching from Mongolia deep into the Middle East and to Europe where a high percentage of the population (like a quarter or more) speaks Mongolian as their native language?

I know that might be true for a small area surrounding Mongolia in Russia, but I think the comparison stretching into the Middle East and Europe is not accurate.

Qinghai is still almost a quarter Tibetan (a percentage that has probably been consistently shrinking in recent history due to migration) and is almost as large, area-wise, as the formal Tibetan autonomous region.