Notice-and-takedown provisions are not just for things that actually infringe copyright, and the "DMCA notice" part may be an extremely easy misclassification of the letter sent to GitHub. More specifically, notice-and-takedown is for user-submitted content that is illegal or tortious to knowingly distribute. Copyrighted content is the main offender here, but there are other categories, especially "anti-circumvention" tools illegal under other provisions of the DMCA.