What does fusty mean?

You are correct!

From our dictionary:

fus•ty

Pronunciation: (fus'tE), [key]
adj., -ti•er, -ti•est.
1. having a stale smell; moldy; musty: fusty rooms that were in need of a good airing.
2. old-fashioned or out-of-date, as architecture, furnishings, or the like: They still live in that fusty, gingerbread house.
3. stubbornly conservative or old-fashioned; fogyish.