What is the purpose and effect of using knuckles when kneading bread dough?
I don't think that it is really necessary to use your knuckles. Rather, there are ways to knead dough well, and ways to knead dough badly. I have seen ineffective people pinching the dough, or turning it between their hands, or other strange motions, which in a cargo-cult way resemble actual kneading, but don't do anything useful. 

My guess is that whoever writes such instructions has learned a correct way of kneading that involves the knuckles, and writes down the admonishment to remind people that they have to do it right for the recipe to work well. The reason for the choice of label may be because the author is unaware that there are effective kneading methods which don't use the knuckles, or because the author has taught new kneaders and has found out that "use your knuckles" is a good cue to get them to use the right kind of motion. 

A third possibility is that the author is referring specifically to the punching down step of a double-rise bread process. In that case, the motion between the first and second rise is not the same as standard kneading, and maybe the author wanted to underscore the difference.