> Like they kinda seem like an unnecessary middle-man between the archive and archivee

They are the middlemen that collects the data to be archived.

In this example the archivee (goo.gl/Alphabet) is simply shutting the service down and has no interest in archiving it. Archive.org is willing to host the data, but only if somebody brings it to them. Archiveteam writes and organises crawlers to collect the data and send it to Archive.org