Yekke2:
“שינוי מקום or hesech hada’as” makes a difference for the same reason that a beracha acharona makes a difference – they are halachic mechanisms via which the person shows that he is “returning” the food to Hashem. I don’t think they particularly have to utilize the dinim of kinyanim because I think the whole concept is more metaphorical (or perhaps metaphysical) than actually a literal kinyan from God and then back.
(I’m sort of deliberately ignoring the “why?” and framing it as a “what?” in classic Brisker fashion. So you can’t really ask why a given act represents “returning”, but you can ask what the gedarim are.)