> You are free to use this software in any way, for any purpose.
This is a license. It can't possibly be anything else. It's a simple, permissive license, but it's a license. Them claiming it isn't a license is nonsense.
> Is public domain a license, or is it no license?
Public domain means nobody owns the copyright to that work. Anyone can use it for any purpose whatsoever, because there's nobody to tell them they can't.
So, no, it's not a license. It's putting something in a category where a license wouldn't even make sense.
A public domain dedication is a statement intended to create that legal status, but may in legal effect be actually a form of gratuitous license and/or promise not to sue.
> You are free to use this software in any way, for any purpose.
This is a license. It can't possibly be anything else. It's a simple, permissive license, but it's a license. Them claiming it isn't a license is nonsense.