Alright, this is a big explanation, so be a little patient.
Raw emotion is, comic wise, one of the strongest sources of power in Videoland. Anyone can have an emotion intense enough to power, say, a city, or do extroadinary feats. But it takes someone particularly skilled to actually channel this energy; Yoshi is already capable of doing so due to his position as Guardian of the Triforce. Other beings like him (Such as Knuckles the Echidna or) can do it as well, along with people particularly in touch with items that use emotional energy (Such as Shadow the Hedgehog and his connection to the Chaos Emeralds). Aside from that, it takes skill to do it.
In this comic, Yoshi uses a combination of his love for Ruby and his sorrow at Grey's disbelief to accidentally trigger his own memories in Grey's mind.
Oh, and whoever can tell me what song fairy boy up there is singing will get 50 points, as long as they get in first.