These chess pieces have laid undisturbed for a long time (15-20 years?). In this time, they seem to have grown clear/white, spiny, long crystals. I'm wondering if they are dangerous, but also curious to know what type of mineral both the chess pieces, and the spines, are made from.
Here's an answer from a curator in a mineralogy museum:
I'd go for soluble Ca salt eg acetate formed by reaction of limestone chess pieces with organic acids in nearby materials?
Growths like this are quite common in museum specimens. The Ca acetate mineral calclacite was first discovered in this way: https://www.mindat.org/min-862.html
Unseasoned oak furniture is blamed for this kind of thing.🌳🗄️
I'll add that it does seem like limestone. I think I can even identify fossil-looking things, particularly in the top chess piece.
Even though at first look it might seem like asbestos, it's not. Refer to the comments on the original question for my opinion why.