It's been a long time since I took a class on disability law (ADA and IDEA) and I'm sure that my explanation will make a lawyer cringe, but I'll do my best explain the rationale. Federal law requires that public and private venues provide accommodation to attendant individuals with disabilities (there are of course exceptions). This covers wheelchair accessibility, closed captioning devices at movie theaters, the sign language interpreters for live speaking or performances that we're specifically talking about, and much more.

Of course, sign language interpreters aren't booked for all public performances in the off hand chance that someone will be in attendance and require the service. Instead, it is the responsibility of the hearing impaired individual to tell the company or organization that they require accommodation and then the burden is transferred to the company and they are required to book sign interpreters, even if its for a single individual.

Anyways, all of this is rooted in our (assuming you're in the US) ideals of equality and civil rights. The Americans with Disabilities Act (which provides the sign language interpreter in the video) is very closely modeled after the Civil Rights Act of 1964 and so to withhold reasonable accommodations is considered discrimination. Deciding what constitutes "reasonable accommodation" has been the primary point of interest in legal cases involving the ADA since it was passed, but the precedent for this type of accommodation is so formidable that to challenge it would be foolish.

Anyways, to directly answer your question, sign language interpreters aren't just for deaf people (there are very few who are truly deaf, but some enjoy the physical feeling of sound vibrations, something you would get a lot of from the bass in rap), but they're also for those with hearing impairment. If someone has profound loss in the mid-range of human hearing, then it will be impossible to hear human speech, but they may be able to pick up high and low frequency sounds. More moderate hearing loss paired with the correct assistive device could allow a person to hear resonably well, but if they rely on lip reading for language comprehension, it could difficult to understand a person with a microphone obscuring their mouth or turning their back. Or it could be a deaf parent accompanying a hearing child to a concert.