It's an operator precedence parser, which is actually quite a bit faster than recursive descent for expressions when operator precedence is defined using grammar productions that would otherwise get turned into methods.
For example, a simplified expression operator precedence can be expressed like this (where {} denotes repetition, implemented with e.g. a while loop in a recursive descent parser (RDP)):
expr ::= term { '+' term | '-' term } ;
term ::= factor { '*' factor | '/' factor } ;
factor ::= '-' factor | <number> | '(' expr ')' ;
Typically this would be parsed in RDP using expr(), term() and factor() functions, where expr() calls term(), term() calls factor(), and factor() calls expr() if it sees an opening parenthesis.
The trouble is that this means that every single expression parse needs to call through this deep code flow before it can see a single interesting bit of the expression being parsed. Parsing "2 + 3" will result in 5 function calls: expr, term, factor, then term and factor again.
The operator precedence parser presented avoids this deeply nested set of calls before it starts parsing interesting things.
This problem is far more acute in a language like C, which has lots of precedence levels, than it is in a language like Pascal, which only has a handful.