yes, I can't speak to the specific algorithm google uses for account lookup, but if an email comes in for firstnamelastname@gmail.com and it doesn't exist but firstname.lastname@gmail.com DOES exist, google will send it to that mailbox.
So, it seems likely the other person still wrote their email address down wrong - but it wasn’t the periods that they got wrong. If this is the case, then I can’t see how there is anything google could do to fix this situation.
FWIW I have <first initial><surname>@gmail.com and get loads of email intended for <first initial><their middle initial><surname>@gmail.com, apparently they just keep writing it wrong.
So I very much doubt the person put their email in incorrectly, but I understand your point.
The exact mechanics of how it happened I don't know, but I very much disagree with firstname.lastname@gmail.com and firstnamelastname@gmail.com resolving to the same address.
m.y.n.a.m.e@gmail.com and myname@gmail.com and my.name@gmail.com all canonicalize to the same account.