As with all styles things differ. Never heard yonkyo described the way you mention either.
1.)Yonkyo as Oshima Sensei taught was application of striking then an upward pressure to the radial nerve from sankyo. Bassically a fast pain compliance to take uke to ground from sankyo.
Obtain good sankyo (uke on tippy toes and maybe 1/3 a backward rotation to off balance), inner hand maintains sankyo esp if pinky hooks ukes pinky, then
release outer hand (choice here is, to slide up to radial nerve or fully release momentarily to strike radial nerve). Using the base of index finger strike/press in then ggrrriind the radial nerve into the bone (pret near same place ODM would take middle pulse), Pain ensues, use ekes arm as sword and take to ground. For submission repeat the in and 1/4 inch up grind. So it can be aid to pain compliance for throw and replace pin to get uke to tap.
Counter is to curl hand to fist, the muscles help blockade the nerve from offending pain. of course tried as sankyo is applied that curled fist...leads to goykyo
2.)Goykyo is what sounds like you observed during demo. Goykyo like combo of an inward bent sankyo into ikkyo (tenkan or irimi) easy to envision, uke resists early and makes a fist before sankyo fully applied, inside hand grabs wrist (chance to grind same area as yonkyo) while every bouncers fav. wrist bend is applied Elbow points up and foward (so uke thumb faces YOU not, his own mid section , this I believe is a difference from the 'std come along' many perform)
gokyo as given to me also allowed uke on tippy toes, twist flexed fist inward for 1/3 rotation... and the kicker was pain compliance by shoving your Thumb into the nerve between uke thumb and forefinger (PS this PP is called Gokoku in Japanese...I believe, easy to remember as PP to apply so similar).
Uke on ground, twist arm, driving shoulder into ground like screw, applying Gokoku, loosens muscle to apply PP at radial nerve as in yonkyo.
3. As to the idea of "is it Aikido" if PP are used well the aetemi are generally directed at vital PP and as I mentioned in Post after moderator Ames shifted it to the Aikido forum
Having taken Ukemi from Oshima Sensei I reflect two thangs
thets A.)extremely powerful fingers and...well hands/arms yadayadayada point too...
B.) With only some dan rank during testing was the same power, control and pain compliance obtained...so, not wishing to dubate wit flok it is my.....
***Experiential world in Ki Aikido w/ Oshima Sensei and other schools of blatant PP use which lead me to BELIEVE, I do believe, that PP control during a locking and some 'Harmonizing' throws (Not Atemi talkin bout here) is part and parcel of the Aikido of The Founder...why dont we hear about it?
Experience over a lifetime.
Tohei Sensei may have branched off but Train w/ O'Sensei oh for a while:)
Oshima Sensei when I was working with him had trained 25-30 yrs w/ Tohei Sensei and a good part as Uchi deshi.
So few people are willing to dedicate, with utter humbleness, a lifetime to one Art and Trust One Master that those are the only people who reach this level of understanding. Why should it be given away? Takes time to assess a person and even then we never truly know one another.
Just MHO. I Hear a set of knives all being honed, hark am I the roast for sup today??
-Karl. Abundant Peace