I don't think anyone knows who runs archive.is. I've tried looking into it a couple of times in the past but there is surprisingly little information to be found. It must cost thousands if not tens of thousands a month to host all that data and AFAIK they do not monetize it in any way. From what I gather it probably is some Russian person as there were some old stackoverflow conversations regarding the site that lead to an empty github account with a russian name. Also back in 2015 the site owner blocked all Finnish ip addresses due to "an incident at the border"[1]. Finnish IPs have since been unblocked. It appears the site owner somehow thought he could end up in EU wide blacklist which seemed like very conspiratorial thinking from him.

1: https://archive.is/Pum1p