KC -- I think it is a pill box too, but not because of the size of the compact. I collect modern and vintage/antique compacts, and some of them are very small. They really are jewelry/accessories, rather than utilitarian items. When you pull out a Swarovski crystal encrusted compact in the shape of a seahorse, or an American flag, or whatever -- it is more of a fashion statement than a true need to powder one's nose.
Back to the compact -- another reason why I think it's for pills is because it would not be a very efficient loose powder compact. It appears to have no proper latch. No woman would want her compact to spill open in her purse, covering everything in dust. All compacts I've seen, even rather old ones, have a latching mechanism to keep the powder secure. Most 20th century compacts also have a disposable/replaceable insert (with its own latching mechanism) for pressed powder, which creates additional security for the product.
