What is the ruling on listening to music in educational videos integrated into English language curricula, and is the student sinful if he remains in the classroom while it is playing, and what is obligatory to do about that?

There is no difference between the ruling on someone who devises a curriculum and the ruling on a student who is compelled to study it. The student who needs university education should fear Allah as much as he is able. If he is compelled to attend a course that contains musical instruments (ma'azif), then there is no blame upon him. However, if he is able to be absent from it, then he should not attend it.