That exception is only during the last 20 years of the term of copyright. The copyright extension was for 20 years, so basically the exception kept the old rules for libraries on stuff that wasn't commercially exploitable.

It's possible that the magazines were published without a copyright notice; and the works were not registered. It wasn't until March 1st 1989 that published works were automatically granted copyright. It's also quite possible that the owners of the rights have granted distribution rights to the Internet Archive; that is common too.