I guess it's possible to use it to refer to just another person not turning up for a pre-arranged meeting, but it is certainly more usual that it's used in the dating sense.
However, it would not only be used to refer to the opposite sex. Both heterosexual and homosexual people date, so any instance of the person you have arranged to meet for a date not turning up would be referred to as being stood up, regardless of your or their gender.
I can't think of another phrasal verb that means exactly the same thing.





