In the German variant, Flohspiel, the "shooters" were often rectangles, and the "winks" were round.

Thank you! Re tiddlywinks, we questioned the amount of different-sized rectangular pieces, but I guess that makes sense if it's a variation of the game.

The owner also questioned the material of the colored pieces, knowing they were too old to be plastic. After doing a little research, I think they must be celluloid, right?

Most likely....and in my experience, the winks often got lost....as you "squidged" them intgo the dark corners of the room. And when kids pick up a game, all the pieces don't always get put back in the box.

Various plastics were known in the early 12900s. Bakelite, for example, was popular for costume jewelry

During late winter when everyone is getting tired of winter, in my area, a few bars hosts tiddley winks tournaments. It done as a 'tongue in cheek' competition.