I agree but I'm still skeptical a little. I don't think in every instance that chakra is disturbed can it be considered Genjutsu.
If that's the case, technically we could call the Hyuga's gentle fist a genjutsu too.
They can pinpoint their chakra and strike your chakra points to disrupt your chakra flow too. By the definition provided that could be considered yin release too.
Now I guess you coul say that since the gentle fist also causes harm to the body then it doesn't fit the definiton but there are two things wrong with that.
Remember when Itachi used Tsukuyomi on Kakashi and Sasuke? It put them in a coma, which happens when there's an injury to either the cerebral cortex, recticular activating system (RAS) or both, which are located in the brain, a physical organ.
Also referring to your own example with Kakashi and pain, you can see that pain had to actually phyiscally insert his chakra rod into Kakashi first, which caused damage to Kakashi's shoulder. Without that rod, Pain can't influence your chakra in any way. He needs to physically insert a chakra rod in you in order to connect his chakra with your system
I could be missing something but I would say that the Rinnegan simpy has some chakra altering traits. I wouldn't say it can perform Genjutsu. Unless ofcorse you would say the Hyugas can too.