thanks Fred...... well, you learn something new all the time on this very informative forum.
I played chess with my sons when they were young, but don't recall using the word rook, which apparently is borrowed from the Persian 'rokh' - although I have heard of the word before. Probably being philistines, I think we called that piece a castle, although it seems this "is considered informal, incorrect, or old-fashioned" .......... well, always knew I was old fashioned - but I'd certainly agree with Neil that the shape does make you think of a chess rook/castle.
I can't quite visualize the workings of this piece , so unsure if this is supposed to be a form of combined match box/striker or just a box as the description says - it doesn't have the usual granulated looking surface of a striker - whether there is a removable top I'm unsure, and there must be a purpose to that channel/slot on the very top. At the time of this Registration, smokers carried vesta cases/boxes, although have an idea that the non-safety match was unpredictable and they could even combust by rubbing against each other, so there were such things as safety cases/box for matches, whatever they were.
I suspect this is a rare item - doesn't look as tho anyone has found one, at least not in recent times.