London Pneumatic Despatch Company
en.wikipedia.org
en.wikipedia.org
https://www.quirepace.co.uk/products/pneumatic-tube-systems/...
Letters, cans of beer and indeed cylindrical foods such as hot dogs, burritos or fish and chips wrapped in newspaper, could be inserted into a cylindrical capsule and delivered anywhere in the network area in a matter of minutes.
The original article is more like a pneumatic cargo wagon. Pneumatic posts of much smaller diameter existed all over Europe before and after the larger one described in the OP:
https://www.warwickandwarwick.com/resources/articles-library...
Plus, it would be pretty simple to adapt internet routing architecture to the tube sorting machines. As long as you can embed a destination (node and endpoint) address in a barcode or NFC tag on tube ingress to act as your "packet header" you can leave the routing decisions to the tube sorting machines much like existing interior gateway protocols.
http://www.douglas-self.com/MUSEUM/COMMS/pneumess/pneumess.h...