"Someone is at the door asking for you."

"What do they want?"

This is the standard way to refer to an unknown person in English, anything else sounds awkward. "What does the person want", "what does he or she want", "what does this 'someone' want", none of these will sound natural to a native speaker.

It's called "singular they". It's used like: "We have a new joiner in our team! They became the talk of the town very fast". I love this feature of the English language, while a bit confusing at first, I think it works much better than "he/she" or "s/he" when talking about someone with an unspecified, unknown or unrelated gender.

This really shouldn't be some surprise. You probably do it on a regular basis without noticing. Shakespeare uses it in Hamlet:

There's not a man I meet but doth salute me As if I were their well-acquainted friend

English has always used the singular they, especially (but not always) when the gender of the target of the pronoun is unknown.

ƿrong. "they" is norþmannisċ. It sċuld be he, forðat hē and hēo ƿuld'fe melded into he, and forðat Englisċ is an Indo-Europisċ tung, ƿere ƿerelie is ðe first kin.

Interesting read about the topic: https://www.oed.com/discover/a-brief-history-of-singular-the...