Though you're correct about Telluride Regional itself (at 9,078' elev, 'the nations's highest airport) which has a 6900 foot runway and can be hairy for take-offs and arrivals, this accident was at MontroseRegional. Montrose is at 5,800' and has a 10,000 foot runway.
Something nasty happened on their takeoff roll, sounds like to me. God bless the aircrew, and may He watch over any survivors.
You're close, but Lake County (Leadville - KLXV) is generally considered to be the nation's highest , although with a slightly shorter runway. (9927'MSL, 6400' x 75' as opposed to 9078', 6870' x 100').
Both have instrument approaches, Leadville has an RNAV departure which is most interesting.
Telluride has an MDA of approx. 2500' AGL. The mountains to the west are up to 5,000' above field elevation.
For the uninitiated, those high elevations are more of a problem in the summer than in the winter (density altitude). On a hot day, some planes just won't get in the air there.