The HBO video focused on Princeton. HYPSM… type colleges are very different than SJS and most publics in major preference. The Harvard lawsuit found very small differences in admission preference by major, smaller than almost any other analyzed admission criteria and in some cases negligible. Rather than make popular majors have far more selective admissions as SJS does, HYPSM… type colleges tend to let major size grow as demand changes. For example, Harvard’s website indicates the number of CS concentrators has increased during each of the past 10 years that are listed, growing from 94 students to 494 students in 2017 – a 5x increase in students pursuing the major and on pace to become Harvard’s most popular major in the near future.
However, I agree that there is not enough information to estimate chances, and major selection contributes to the admission selection, including how the major selections fits with the rest of the application. If you want to pursue CS, it helps to have an application that suggests you are strong in math/science/CS including top grades in highest available level courses, strong math//science test scores, math/science/CS ECs/awards, LORs and essays supporting a math/science/CS interest and talent, etc… much like the CS Princeton acceptance kid I listed earlier.