I love tribbles. The Trouble with Tribbles episode and the scene you shared, is one of the funniest in all of Trek lore. If you type "The trouble with" into a search engine, this reference still pops up. I did a little background search on the tribbles and I'm including it here. I am a research nerd.
Also, the writer of this episode realized that the tribbles were more than a little inspired by the flat cats in Robert Heinlein's Rolling Stones. A waiver was needed for the tribbles episode to air, and to keep them from getting sued. They then had the issue of how to make a tribble.
The use of live animals to represent the tribbles was immediately ruled out. According to Gerrold's account, the inspiration for the form of the tribble instead came from a fluffy keyring owned by Holly Sherman.
[13] Sherman's Planet in this episode was subsequently named after her.
[42] The design came from
Wah Chang,
[43] but they were individually sewn by Jacqueline Cumeré. She was paid $350 to sew five hundred tribbles from synthetic fur and stuff them with foam rubber.
[13][44] Six ambulatory tribbles were made using the mechanisms of walking toy dogs, which were quite noisy and required the dialogue to be looped in during editing.
[45] Other tribbles were created by Jim Rugg out of
beanbags for when it was required for one to sit on a person or object, and the breathing tribbles were hollow with surgical balloons inserted.
[13][45] Some of these tribbles were later displayed at the
Smithsonian National Air and Space Museum in Washington D.C. in 1992.
[46] The sale at
Christie's auction house in 2006 included tribbles from this episode as part of a larger
Star Trek sale.
[47] Because of the synthetic fur technology of the 1960s, relatively few original tribbles exist as of 2010 because the fur fell out over time and they went bald.
[48] An original tribble was sold at auction in 2003 for $1,000.
[49] (Wiki)