I just spent about 15 minutes searching all sorts of US government websites including the Library of Congress. I could not find any mention of the Internet Archive anywhere. Do you have a specific source that verifies that IA is a library?
No I just meant that the government sets the standard for what qualifies as a library. I'd have to take a trip to whichever city IA is based out of and check the public records to determine whether or not they've filed for library status.