The total length of input to a pushdown automata which accepts by empty stack is an upper bound on the number states and stack symbols
That section is not talking about parsing. The algorithms referred to are algorithms for converting between CFGs and PDAs of different types. The question is, as usual, "what is the computational complexity of the algorithm", and the response is, as usual, expresseded in terms of the size of the input -- to the algorithm.

The input to an algorithm which converts a PDA to a CFG is the PDA, and the size of the input -- the metric stick for the algorithm's complexity -- is the size of the *PDA". That's what the authors intend n to be.

How does one measure the size of a PDA? Simple: you write the PDA out as a string in some PDA definition language, and count symbols in the description. That's a completely fair procedure, because in order to call the conversion algorithm on the PDA, it's necessary to give the converter an input which represents the PDA.

Given that definition, the claims are not at all surprising. Every state and every alphabet symbol must be present at least once in the PDA description, so the size if that description is an upper bound. Similarly, it is possible that most of the description of the PDA is the description of a single rule, which could push almost n symbols.