Oh well that's younger than i expected as an early millenial, but i think of "puter" as a term from that cross-generational group i've heard described as "analogue childhood digital adolescence". If you were also watching vhs as a kid it sounds like that includes you.

Do you remember, IRC, the sweet song of the modem and the pain of a parent picking up the phone while you were online? That's what i think of when i hear Puter.