If you want to peek behind the curtains, Probnot posted the code on github (and adds that this code was loosely put together—please be gentle). The script pulls current weather information from Environment Canada and formats the data into a vintage-looking display.
In the video example, the Raspberry Pi display is output to an old CRT. According to Probnot, this was accomplished with RF modulators connected to the cable in his house. The number shown in the corner is the actual UHF channel.