To me it boils down to (pun intended)

> Traditional dictionaries skip almost all such phrases, because they contain spaces.

Yes, because they're phrases, not words. I don't even understand what's surprising about this. Sure, the entire article talks about how dictionaries contain _some_ phrases; but it's clear it's not many of them. Dictionaries are for words, not phrases.

Technically they are both phrases and words. You can call them lexemes if you want to avoid confusing the computer programmers who do not understand that life isn't binary.