I've tried to see evidence that she is making the notes in her mouth, but except for the well-known fact that high eyebrows help high notes, no luck.

The Alphorn is a very long natural horn which enables a lot of higher harmonics to be overblown above the fundamental by lip & breath pressure alone. The obvious limitations of such an instrument were overcome by the invention of the slide-trumpet in the middle ages (most favoured of angels!) and later by the sackbut / trombone. Valves came along still later, faciliating another level of versatility. The girl in the video is using her lip & breath pressure alone to excite the natural harmonics of the horn - try it yourself next time you're in a hardware store by blowing a raspberries down a long piece of inch-diameter piping!

'impedance increase affecting pitch' as 'like' muting a trumpet or trombone.

Mutes don't effect pitch - if they did they wouldn't be much use.