It is true regardless. What you are talking about is a language implementation detail that is orthogonal to reasoning about the type system. Depending on your definition (reasonable people disagree and could be contextual), the memory layout is also rarely a concern when modeling type theory.
However, I can't make sense of the idea that "most languages don't have subtypes". Every language I can think of above ASM has at least some. In C, int8_t is a subtype of int16_t, for example.
And the idea that this is new territory... Here they contrast subtypes in C++ to that of "the new language Java".
https://www.cs.princeton.edu/courses/archive/fall98/cs441/ma...
I agree with the comment that OP really should make it explicit what they mean. It presents itself as "what is subtypes" but they unfortunately use the same term for different concepts in the same text, which I guess contributes to the wider confusion in this thread. Inserting a few "Algebraic ..." and making the context explicit in a place or two.
Or put differently: Algebraic subtypes are a subtype of subtypes.