On that Triad Exercise short video he's literally just playing chord tones. Every time the chord changes he plays a variety of that chord that's happening at the time. Nothing but different voicings of the chords all over the fretboard.
The B minor chord is made of the 1-3-5 from the B minor scale.
b (1st) - d (minor 3rd) - f# (5th)
When the B minor chord is happening he's playing those 3 notes in various configurations all over the fretboard. He plays:
1-5-3, 3-1-5, 5-3-1, 1-5-3 (an octave higher)
Then the next chord is F#. That chord is made from the 1-3-5 of the F# major scale.
f# (1st) - a# (major 3rd) - c# (5th)
When that chord is happening he's playing those 3 notes in various configurations all over the fretboard. He plays that pattern down picking up where the B minor went up.
He does that for all the chords.
I have a collection of tutorials on chord triad & inversions that show how to visualize & play these voicings for any & all major & minor chords.
https://www.guitartricks.com/collection/triads-and-inversions
Next, question: "So is he then switching over to play the respective MAJOR scales? I thought that you usually stay within the main scale- so in this case it is B MINOR. This is where my confusion lies."
Again, it's not either-or. :) It's both. The chords are found in the scale. When you harmonize the B minor scale you get a collection of chords. And some of those are altered to fit the harmonic & melodic minor scales. Hotel California is a big circle of of fifths motion (many of the chord root notes are a fifth apart which is a common harmonic motion technique).
You can look at the entire progression as chords related to the key of B minor.
B min (i) - F# (V harmonic minor) - A (bVII) - E (IV) - G (bVI) - D (bIII) - Em (iv) - F# (V) - B min (i)
Or you can look at the relationship of each chord to the previous.
B min (i) - F# (V of B) - A (bVII) - E (V of A) - G (bVI) - D (V of G) - Em (iv) - F# (V of B) - B min (i)
Both ways are mutually reinforcing.
I explain all of these concepts in my tutorials on harmonizing the major & minor scales & the improvisation collection.
Hope that helps!