Well... I have a weak answer, but it doesn't conform well to the expectation of having exactly two better than the rest.

The words all use at least two letters from the word "THIRTEEN".

And finding words that are more so than the others...

Clearly THIRTY-SEVEN is the winner, using all 8 letters, but VERTICALITY and INERTIA can each source 5 of their letters from THIRTEEN (not counting letters more times that they appear there), so I actually end up with three words "better" than the others.

I had something better, but it breaks on a few words and I can't see how to rescue it.

So here is my "better answer", rescued from a close idea...

all the words have a consecutive letters that are horizontally adjacent on the QWERTY keyboard:
SADIST
THOROUGHFARE
HYMN
POISED
YU RT
THIRTY-SEVEN
STREWN
VERTICALITY
INERTIA
BALDERDASH
HIGHFLYING
REWARDING
OPINIONATED

and the winning two then are

STREWN and VERTICALITY

And here, for reference, is the acknowledged "weak answer" I tried first:

The words all use at least two letters from the word "THIRTEEN".

And finding words that are more so than the others...

Clearly THIRTY-SEVEN is the winner, using all 8 letters, but VERTICALITY and INERTIA can each source 5 of their letters from THIRTEEN (not counting letters more times that they appear there), so I actually end up with three words "better" than the others.