This a game I had not heard of before - evidently a CW version of pinball, and just as popular with the boys. Vintage boards are found online and according to Wikipedia:
"Bagatelle (from the
Château de Bagatelle) is a
billiards-derived indoor
table game, the object of which is to get a number of balls (set at nine in the 19th century) past wooden pins (which act as obstacles) into holes that are guarded by wooden pegs; penalties are incurred if the pegs are knocked over. A bagatelle variant using fixed metal pins,
billard japonais, eventually led to the development of
pachinko and
pinball."
The author below mentions it's use in a Union hospital as entertainment for the patients-
With another gift of tools, the boys in Ward 20 knocked up a nice little bagatelle board with glass balls and a cambric cover. Ward 6 went over to inspect and imitate. … but I promised them that if they would make a first-rate board, they should have all that was necessary. So they went to work, and the result was a beauty. The table is seven or eight feet long, covered with scarlet flannel, and with turned balls and walnut cups, and the men of the ward have enjoyed every minute of its existence for the past month. I have never gone in when there hasn't been a crowd round the table pushing balls or keeping count, and I really think that the health of the ward has improved under the treatment.
Source: page 496-497