It isn't dairy, that is correct. Note however, that using the term 'milk' to plant liquids has hundreds of years of history in the English language.
Happy I was a bit careful with that comment.
For instance, I noticed recently that a drink that said it contained "natural flavoring" had sucralose in it. I guess sweet isn't legally a flavor maybe, but from the perspective of a consumer, it's hard to tell if this sort of thing is caused by finding clever loopholes or just by ignoring rules completely.
You can't fall back on "just read the label" when you're given a mixture of contradictory, inaccurate, or ambiguous information that is training you to ignore the label.