They wouldn't use the name "cordial" because it has a different meaning in the US. Over here, "cordial" is some sort of flavored alcohol, usually with a sort of connotation of something that rich people drink after dinner or as something refreshing that some rich people on a southern plantation might drink. (so it's not only alcoholic, it's classist/elitist, too)
They wouldn't use the term "squash", either, as to most Americans, that's a vegetable or maybe a sport that rich people play.
I'm not aware of any specific food labeling requirement, but the term "water enhancer" is fairly well known to Americans who go camping, drink well water, or disaster preppers. It's used as catch-all term for anything to be added to water to improve its flavor.
So it would include powdered drink mixes such as Tang and Kool-Aid, which is why I would assume they specified that it was a "liquid water enhancer" to distinguish themselves from those other things.
But in the past few years, there have been a few companies selling tiny little squirt bottles of flavorings for bottled water. (the first one that I remember seeing was Mio) They're not like liquid drink mix concentrates like what you're describing, as they're typically just a few drops to flavor a bottle (500mL) of water instead of something that's diluted around 1:5, like you would for a flavored heavy syrup.
So basically, not only does 'cordial' not mean the same thing in the US as it does in Australia, but what you're dealing with isn't exactly the same as a 'cordial' from Australia, either.