The author confuses the concept of injectivity and well-definedness. For an injective function f, it has to be true that given distinct a and b, f(a) != f(b). That's not the problem here; rather the problem is that for a timestamp t there's no unique human-readable date x such that f(t) = x. That's well-definedness, not injectivity.
https://en.wikipedia.org/wiki/Well-defined_expression
You could talk about the inverse function, from human-readable dates to timestamps, and correctly point out that that function is not injective, because more than one human-readable date maps to the same timestamp...