@Bootybug As far as the word is concerned, it doesn't actually matter. Reincarnation only means, when written in simpler words, to be made flesh again. In isekai there's a difference between transfer (summoning) and gaining a whole new body. Obviously the MC here got a new body since he's not anymore in the invalid grandpa's body. Though I do understand why you are asking because to be born again would probably be the more natural way of reincarnation.
An Isekai hitting a sombre, melancholy note in the first chapter?
A disjointed set of character introductions without any superfluous expository text?
... is this a trap?...