Nons refer to these four dogs. They're pets on the retired rares list that are often used as a way to measure pet values. For example, you may see someone say (blank) is a worth 2 nons. This would mean the pet they're referring to is valued at any 2 nons.
I'd also like to mention that there is a fifth dog with non in their name, the nonballoon, however it is valued differently from the four I listed above and is not considered one of the nons.