Many proteins other than histones are found associ- ated with chromosomes. what roles do these nonhis- tone proteins play?

As far as I concerned, what they do are :
1. As a regulator. During transcription until translation, this system regulate by so many regulator which make up by protein. You will read more about this in gene regulation topic. How our genome which contain the same sequence in all of our cells can express different fenotype.
2. As a transcriptional factor. To inisiate transcription, these system need that factor to accelerate this step. RNA polymerase will stick to promoter with the stimulation of this factor.