If one is a son, grandson, or great-grandson or beyond, the word "son" applies in Biblical reckoning. The same is true of daughters. This is easy to demonstrate, given the passages surrounding Rebekah.
45 And before I had done speaking in mine heart, behold,
Rebekah came forth with her pitcher on her shoulder; and she went down
unto the well, and drew water: and I said unto her, Let me drink, I
pray thee.... 47 And I asked her, and said, Whose daughter
art thou? And she said, the daughter of Bethuel, Nahor's son, whom
Milcah bare unto him: and I put the earring upon her face, and the
bracelets upon her hands. (Genesis 24:45,47, KJV)
Notice that Rebekah tells Eliezer that she is the daughter of Bethuel, Nahor's son. That means she was the granddaughter of Nahor. Now look at the next verse.
And I bowed down my head, and worshipped the LORD, and blessed the
LORD God of my master Abraham, which had led me in the right way to
take my master's brother's daughter unto his son. (Genesis 24:48, KJV)
Abraham and Nahor were brothers (see Genesis 11:26; 22:23). But Rebekah was not the daughter of Abraham's brother (to our reckoning), she was his granddaughter--yet Eliezer refers to her as Nahor's "daughter."
This shows that generational gaps were lightly regarded when considering family ties.
However, there is another possible phenomenon here. No mention is made of Rebekah's father interacting with Eliezer or the family at this time. Apparently, he has already passed away, for if he had been living, Abraham's servant would surely have asked permission of the lady's father to take her with him to Isaac.
In the society of that time, with their father having already passed away, Laban, the only son mentioned, is now man of the house. As the patriarch of the family, he is the authority figure, even though he is young. So it is his prerogative to decide the case of his sister, and therefore the focus of "they" (Rebekah's family members) falls centrally to him. This would help to explain why "sister" applies.
But supposing the text had said "sister and daughter" or something of this nature; would that not cause the reader to think that two persons were involved in place of one? Evidently, Moses expected the reader to be intelligent enough to understand the story without superfluous explanations of this nature. The use of "sister" suffices.