This is a maze puzzle: find a way to move the "rook" piece (shown in the second photo,
SOLD SEPARATELY) to its home position (also as shown in the second photo). Or alternatively, starting from the home position, remove it from the sphere.
The rook piece (in fact a pair of them) are available at
http://shpws.me/SFcK.
Octahedral holonomy maze 2 is another maze that uses the same rook piece, available at
http://shpws.me/SFcL.
If you go around a loop on a curved surface, you come back rotated - this effect is called
holonomy. In these holonomy mazes, the rook cannot rotate in place; you must use holonomy to dodge its arms around the pegs blocking its way and escape!
Note that Shapeways' processing for this material polishes the parts. However, they may still need some working in to move smoothly.
[Update 2021-05-15: slightly extended geometry of the "holder" for the home position to remove a cheat.]