I was watching this:and it occurred to me, is Leia even classified as a Disney Princess now?
I'm aware she may not be included or merchandised in the "family" in the same way, but I'm curious as to her classification.
Yes and no, but more no than yes.
"Disney Princess" is a media brand owned and operated by Disney Consumer Products. As of March 2016, there have been no indications that Princess Leia will be added to the existing lineup of princesses. There are presently no live action princess, nor are all of the princesses owned by the Disney brand part of the existing lineup, indeed the overwhelming majority are not.
Disney certainly seem more than happy to merchandise and operate a brand of Disney related Star Wars products in their parks but they've done so for decades anyway, as part of the merchandising for their "Star Wars: Star Tours" rides, so it's not such a huge shift as you might think.