As Patrick noted in the interview, the rule pertaining to who can see the videos was officially lifted shortly before the pandemic hit. Before that, staffers in the Lortel Room (and I used to be one of them) were supposed to ask each patron to give their purpose for viewing the tape. We were aware that what we were told wasn't always the truth, but we took people at their word. The procedure was required by the agreements under which the videos were made.
Incidentally, although it wasn't specified in the interview, this change of rules does not apply to videos of shows that are currently running, or ones with additional restrictions placed on them. (That is, the ones that require advance permission to view.) It simply means that patrons with an NYPL card can see most of the material in the archive without having to give a specific research purpose.