Debeaking is not generally quite as horrendous as it sounds in that article.

Basically, the premise is to remove the 'pecking' part of the upper beak. It is done because chickens tend to pursue any bare or bloody spot on neighboring chickens often pecking the flesh to the bone.

A de-beaked chicken looks odd because the the ends of the upper and lower beak no longer meet but I have never heard anyone suggest that it remains painful, and I'm not sure how anyone would know. It is certainly no more painful to perform than the de-horning of a bovine.