For a while I've been watching how this stream and its fans are all attached to the team, giving its members affectionate nicknames and praising them/berating them. It just clicked for me now that this is the same effect that hit us as first-time players, or the popular nuzlocke comics subgenre. The only difference is that since everyone is sharing this exact same experience, the effect is magnified thousandfold.
In retrospect, I can't think of a better game for this sort of experiment. Even other turn-based RPGs couldn't replicate this to its full effect unless they were effectively Poke-clones.