Great.
The set is for the game Bizique and the only reason why I bought it was for the counter that came with it is MOP and according to the curator of the Whist counter museum; he has never seen one made with MOP.

Other than that, I have no accurate idea of age and maybe running it by Bizique set collectors, they might know more... or maybe the cards on the box hardware and the cloth lining can help in pinpointing age,

Ì doubt this counter (monogrammed) is part of the set as was a MOP Pot rectangle plaque that I have never seen before and not part of the game since the game is a two-person game.

Thus the $300+ price to you since that is what I paid for the lot.