Exactly. For every level of abstraction, the abstractor is the high level and the abstractee is the lower level. Those aren't real words perhaps, but you get what I'm saying. It's all relative along the chain of abstraction.
Is it a chain though? I think it's more of a branching network that (almost?) always is stopped at quantum physics and it's theories or some form philosophy.
It's not really abstraction though. It is more like syntactic sugar. In stead of 1000111011 you say ADD, but it is still the exact same thing. There is no functional, prgrammatical benefit of one over the other. It's just that asm is readable by humans.
At least thats as far as I understand asm. I haven't gone beyond NandToTetris
I would argue they don't know what that means really. Assembly is pretty much a mapping of words to machine code. It's just a way to make machine code easier to read. It doesn't actually change how it works.
A compiler re-arranges and modifies things so what you write isn't the same as the final program that is created. With assembly it is. It's not really an abstraction, but a translation. It doesn't move you further from the machine, it only makes it so you're speaking the same language.