You're right. In that situation "abajo" would mean "below" rather than "downstairs", and your answer would be correct. But 99% of the time "la familia esta abajo" means "the family is downstairs". It's worth knowing that idiom, and DL's rejection of your answer is helping you to learn it.
John, it may depend on where you live. In the US, we use "family" as a collective noun, which takes a singular verb, "is." Apparently, it's the same in Spanish because Duo uses está.
But, it is my understanding that, in British English, it's considered more like "family members," which would take the plural verb, "are" or están.
It's sort of like I heard on BBC yesterday, "[The team] now advance to . . . ," but on US TV it would have been "[The team] now advances to . . . ".
Last time I heard it was the early '70s in rural South Carolina - I haven't lived around multi-story houses since. So, probably archaic usage or maybe just very localized. Or maybe even just family slang that I didn't realize wasn't common. Who knows? It was a LONG time ago, I'm amazed it stuck with me.