There was a thread on this site once upon a time regarding definitions of aiki I think. It should have some information regarding how some Aikidoka may define the concept. Maybe Jun can help here.
Aiki is a concept, harmony of energy, it may have many manifestations or applications, even within the different schools of Aikido alone. Ki on the other hand is energy in whatever form you like, again viewed differently depending who one talks to.
Aiki may fall into the realm of timing, coordination and a host of other things that deal with harmony. In the event that an Uke is conditioned to respond in certain ways to certain movements without ever being touched, some may call this Aikido (being so in harmony and connected with the energy of the other that the touch is unnecessary), others may not, since it may not work without a willing and cooperative partner who does not exercise their own free will to resist strongly and purposefully.
Going with Bruce's response, Uke's aility to throw himself as a result of self-unbalancing intent and posture happens pretty often in Aikido training, especially with a sensitive instructor who is capable of maintaining such a degree of timing and control. However, in this same light, will these "no touch" techniques work with an Uke who maintains mushin while attacking, or who is so trained to attack that no openings/unblancing are made of Uke's own accord? In my experience, with ki and other styles of aikido - no. Tori has to utilise the principles of Aiki at some level to create or see his own openings for timing, blending, kuzushi and technique. To create one's openings for kuzushi, touch may be necessary with an uncompliant aggressor in my humble opinion.
I guess what I'm saying is Aiki is a concept that can be applied in a martial or non martial sense. I have trained with folks who don't believe Aikido is/was meant to be a "martial art." I don't agree with them, but what they say makes a lot of sense to me as well. It depends on what you want it to mean to you in your training that counts I think.
As far as freezing people in other rooms or at distance.... The Truth is out There! I want to believe.
I think this is more a result of Uke's mind than anything that Nage is doing, just like the no touch throws.
Just my thoughts on the subject.