I've thought a lot about this since Fr. Ripperger's recordings helped me discover tradition.
I'm not sure that his exorcisms are positive proof by themselves that the new rite of Holy Orders is valid. Even father has admitted that protestants and non-Christians occasionally perform successful exorcisms.
Here's what I think really merits some serious thought, and this mostly involves the validity of the new rite of episcopal consecration:
1) Fr. Ripperger claims that the demons he deals with know when he's been given faculties by a bishop to perform a solemn exorcism. I've heard him talk about demons that will ask him, "Where's your authority?" which is a sign that he needs faculties in order to drive the demon out. Father claims that when he returns after getting faculties, he doesn't even have to say anything to the demon; they immediately begin submitting to his authority. This would seem to prove that bishops consecrated in the new rite have authority. Maybe their authority is simply material, but whatever it is, it's effective in the context of spiritual warfare (which is significant).
2) No only does Fr. Ripperger claim that bishops consecrated in the new rite have jurisdiction, he also claims to have received effective faculties for a solemn exorcism from a bishop who was a heretic.
3) Finally, Fr. Ripperger claims that demons react to the Hosts he has consecrated and uses during exorcisms. The really interesting footnote here is that he seems to imply that demons know the difference between hosts consecrated in the TLM and hosts consecrated in the NO. Father claims that ultimately they, "react the exact same way to both," but that they will differentiate between the Hosts, "using various crafty means."
You can hear Fr. Ripperger talk about some of this at about the 11:50 mark of this lecture:
http://www.sensustraditionis.org/webaudio/SW/SpiritualWarfare3a.mp3