A reference for a "more algebraic" approach to pushdown automata and CFLs?
Sakarovitch's PhD thesis from 1976, titled Monoïdes syntactiques et languages algébriques (syntactic monoids and algebraic languages), revolves around this topic.  At the time, this led to the definition of pointed monoids (see, e.g., his MFCS'75 paper).  Around the 80's, the algebraic object of choice to study CFL's shifted to the Hotz group—Sakarovitch even has a paper on that topic in Acta. Inf.  As far as I know, pointed monoids did not get the attention they deserved, although the same ideas can be found in Behle, Krebs, et al.; likewise, some recent approaches, based on more sophisticated tools, especially Stone duality, may provide a sound framework for such studies.  

Another modern approach is that of Clark on the syntactic concept lattice, that I'm not familiar with.

As for the actual intentions of the author, one safe way is to ask him directly.