pak* is not derogatory term in India, most people dont know it is racist slur (to describe all south asians, not only pakistanis)
I have not seen the video, if the guy knew and used it deliberately then its definitely wrong.
Similarly miyan is not derogatory but it is used to describe all muslims (in my place all muslims are called pathan, nobody knows that its only a specific tribe).
The derogatory term for muslims is katwa (the cut one, or the circumcized one). I remember one of my college mate using that word to describe a muslim girl ( although I knew he admired her).