As with "hand" in the other thread, this is not to be taken literally as "house". This meaning in this case comes from the Chinese usage of the word from the middle-ages, meaning someone or some group with specialized knowledge.
The answer to this is similar to your other question about 手. 家 can also have the meaning of a profession or discipline, or the people engaged in it. This abstract meaning can be understood much like 手, as back in the day it would be common for all individuals of a certain line or household to practice the same profession, and thus for the boundaries between the individual and the profession of their household to be blurred somewhat.