It's very enlightening to learn that paper play has been this old. Was this a contemporary of the paper dolls perhaps?
Viewing post in The Tiny Toy Theatre Imagination Kit comments
I don't know much about the history of paper dolls, but I wouldn't be surprised! The English toy theatres emerged from prints that were originally souvenirs of live theatre productions (you could take home an engraving of your favorite actor in their role). https://www.britannica.com/art/toy-theatre
I know that Pollock's also sold some wooden dolls in the same catalogue I scanned as these toy theatres - I'd love to track down more of these catalogues and do some more digging.
I'm also woefully under-informed about kamishibai, a similar kind of paper puppet theatre that emerged in Japan at about the same time (if not earlier). It's something I need to learn much more about as I continue this project!