Yes, that's how the room is known at Lyndhurst. I suppose it got its name because Jay Gould and perhaps earlier owners used the room to play games of cards. The name is even used on many floor plans of the house...
Page 17/Scene 54C - Liz: 'The Old Swimming Pool. David plays there.'
- which, with the exception of adding "And" to the beginning of the first sentence, is delivered as written - but, as we can see given today's capture -