geu jip adeureun ajik eoryeoseo honja jihacheoreul tal jul molla.

In Korean, 집 can mean both:

• a house/home
• the household/family that lives there

So 그 집 아들 is a very natural way to mean that family's son or the son from that house.

This is common in Korean. Instead of using a possessive like their son, Korean often identifies someone through the household or group they belong to.

은/는 is the topic marker, while 이/가 is the subject marker.

Here, 아들은 presents the son as the topic:
As for that family's son, ...

This can sound like the speaker is making a comment about him in particular. It may also carry a slight contrast, such as:

• The son, at least, is still too young...
• As for their son, he doesn't know how to...

If you used 아들이, the sentence would feel a bit more like simply identifying the subject, without that topical feel.