The smell is just of the clothes. New clothes have a smell too if you think about going into a department store. The Thrift Store has clothing that has been worn and washed many times in some instances. Any one that washes clothing knows that clothing after awhile retains smells from the wearer. The washing does not always remove this smell so after a while the smell becomes part of the used clothing. Put a collection of this clothing together along with the fact that it has probably been shoved in the back of a drawer or closet and as such get that packed away smell in addition so mix it all together, Thrift Store!
In my State, Indiana, they require the clothes to be dry cleaned or steam cleaned or washed in bleach. What you smell is the residue of the dry cleaning solution used to make certain there are no bugs or bacteria on these clothes. There is also a mustness to things like baskets, that have been stored in garages and attics.