I think the non-milky ones are usually called sorbets, but for example small fruity ice creams on sticks we still can ice creams and these don’t have milk. So I guess my answer is no we don’t (in Europe).
In the US we also have sherbet which is made with dairy; but we don’t label it ice cream. So I’m guessing if we even have a legal ruling about it, it might not have anything to do with how much dairy is in it.
Also should add that my favorite non-dairy frozen thing is Rice Dreams. Which is like ice cream, but made with rice. It also doesn’t claim to be ice cream.
We colloquially call a lot of things I’ve cream that aren’t labeled ice cream, and aren’t legally ice cream.
The US has tediously long definitions for different foods, and ice cream needs specific proportions of milk products, as well as limits on other physical properties.
https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/cfrsearch.cfm?fr=135.140
https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/cfrsearch.cfm?fr=135.110
https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/CFRSearch.cfm?CFRPart=135
So while I might pick up some sherbet and say “I got ice cream”, and people would know what I meant, it would never be labeled ice cream.
I also like oat milk ice cream, but it’s actually labeled “frozen dessert” because it doesn’t contain dairy.
The company isn’t allowed to use a term that might mislead a unwitting or uninformed consumer, but the consumer is free to have a more relaxed definition, and stores can put things where you would expect.
