I was contrasting it against table-driven parsers (e.g. typical of the Yacc/Bison type) which I believe don't have any recursive calls and use a separate stack, while this one does make recursive calls. In some ways operator precedence/precedence climbing is like an optimisation of RDP, replacing a set of recursive functions with a level counter and a loop.
I can view using the CPU stack instead of an explicit stack, and the CPU instruction pointer instead of an index into a state table, as optimizations too (direct encoding). There also exist recursive ascent parsers, which are the RDP analogue of table-driven LALR parsers you're talking about.
Point being, there are a lot of different parsing approaches, with pros and cons, and it can be useful to treat them separately rather than view them within only a couple of lenses.
