You might argue that anything in "waltz time" is a waltz, but then your argument becomes circular. You would be saying it's a waltz because it's in 3/4 time and it's in 3/4 time because it's a waltz.
Possibly it makes more sense to musicians to notate it as 6/8 because the triples come in pairs. It's still a waltz though, and dancers' instinct will be to break it into triples. It's not hard to scramble a 6/8 signature to make it not a waltz (don't put downbeats every three, and it isn't a waltz) but that song definitely doesn't do that.
For this piece, I think it's a waltz because it's in 3/4, at a typical waltz tempo, and it "feels like" a waltz, which is to say that the emphasis on the beats and their precise timing feels like waltz music usually does.
So no, I would not argue that anything in "waltz time" is a waltz.
Just as a sanity check, I decided to look up some sheet music and see how others have interpreted the song. Every single one that I can find notates it in 6/8 (interestingly with some individual measures in 9/8).
If you write it in 6/8 instead, many musicians will emphasize 4 less than 1.
I think that dancers knowing music and musicians knowing dance is extremely useful. It changes your opinions about notation.
Whether it makes more sense to musicians write it 6/8 or not, I have no idea, but it's still a waltz.