I disagree with this note, even though I often read Dijkstra's notes for enlightenment. The pigeonhole principle is one of the basic tools we have to approach mathematics, and therefore deserves a name. We often assimilate proofs by "abbreviating" the major steps through naming them - "pigeonhole principle", "passing to subsequences" etc.

Even in the realm of "infinite" mathematics like analysis, theorems like the Heine-Borel Theorem and the Bolzano-Weierstrass theorem rely on pigeonhole-like arguments. Of course, that statement can be made rigorous in reverse mathematics.