When Moss shows Roy his tear solution, the mini fridge has a "Guided By Voices" sticker, referencing when Jen admitted she has become a fan and a "nerd conduit."
During the Channel 4 News (1982) broadcast where Jen and Roy's identity gets revealed to the world, on one of the photo shots you can see the house/parish that was used in the television sitcom Father Ted (1995). Father Ted was co-written by The IT Crowd writer Graham Linehan and Arthur Mathews.
'Game Board' is based on the web series The Dice Tower (2006). The phrase "shut the fridge" in the second video is based on The Dice Tower's catchphrase, "shut the door," which appears at the end of many of their videos. The game designer's name "Reina Knitsky" is a play on the real board game designer Reiner Knizia.
When the screen starts piling up with memes made about Jen and Roy, one of the photos has the parochial house from Father Ted (1995) in the background. Graham Linehan, writer of The IT Crowd, co-created Father Ted.
When Moss changed his clothes in a telephone booth, it is a spoof on the Superman comics in which Superman famously changed into his uniform in telephone booths fast enough that no one noticed.