Sonnet's RackMac mini[1] puts two unmolested minis in a short 1U enclosure: sixty minis in 30U. A web search turns up the Apple Mac Mini Relay Rack Shelf[2] from RackSolutions, which has four minis in a full 1U enclosure.
I'm willing to believe that there are cooling and airflow advantages to the sleds, although those two small fans at the back of the sled don't look too exciting. The biggest advantage seems to be cable management and the ease of sliding out a single mini at a time.
One comment on the video points to another video[3] about MacStadium, which mounts minis sideways on what look like library shelves.
[1] https://www.sonnettech.com/product/rackmacmini.html