A few structural forces stack on top of each other here. First, limited buildable land: much of Routt County is national forest, ranchland, or constrained by terrain and water, so supply can't expand quickly to meet demand. Second, destination-resort demand: Steamboat draws buyers from outside the region who compete with local buyers, and resort-town demand is national, not local. Third, remote-work migration: the shift to flexible work let more people convert a vacation into a primary or hybrid residence. Fourth, second-home and turnkey demand: many buyers want a furnished, ready-to-use property and are less price-sensitive than primary-residence buyers.
Those forces push demand against a supply that is slow to grow. For the actual appreciation figure, see the Steamboat Springs Board of REALTORS® reports, the MLS, and the FHFA House Price Index.