] What was it about this game that made it so innocent? Was there perhaps no gambling involved, or was it something like "Go Fish" or "Old Maid"?

Based on the paragraph following, I suspect it must have been the sort of card game that contained no gambling or required concentration so no idle chat would befall the women:

"...moralists waxed monotonous on the unfortunate trade of female visiting. Visiting drew women from their duties and encouraged idle chat or worse scandal."

Sheesh, some people just don't want any of us to have fun! ;-)