Why isn't Modus Ponens valid here

Note that $$(\lnot A \lor B) \rightarrow (\lnot A \lor B) \equiv \lnot(\lnot A \lor B) \lor (\lnot A \lor B) \equiv \top$$ In other words, the first premise is a tautology. It says nothing more than "either $\lnot(\lnot A \lor B)$ or else $(\lnot A \lor B)$ holds. And in assuming the law of the excluded middle, one of the two disjuncts must be true, and thus the entire statement is tautologically true.

The second premise is $\lnot A \lor B$.

The argument then can be stated as follows:

$\quad \top\tag{premise 1} $
$\quad \lnot A \lor B\tag{premise 2}$
$\therefore \lnot A \lor B\tag{repetition of premise 2}$

So the conclusion becomes a reiteration of the second premise.

Perhaps that is what your book was attempting to convey?

To infer $p$ from $p \rightarrow p$ and $p$ is a legitimate application of modus ponens. It isn't a particularly useful inference, but it is a correct one.