I watched the episode (on hulu) to check the sets (it was from 1960). Although there is a slight similarity (the doors are stage-right, the fireplace centered), I didn't see anything else to indicate they were the same. I'm thinking, back then, many stage-sets were formulistic based upon available space.
TZ made only about a half-dozen episodes switching from film to video (and then transcribed onto film) in an attempt to save money. In the long run, for various reasons, it didn't work and the experiment stopped. The most famous of them is "Night of the Meek" starring Art Carney as a homeless department store Santa who gets fired on Christmas Eve for being tanked. Surrounded by cold, impoverished children who break his heart because they think he is Santa and there is nothing he can dor for them, he discovers that there is a certain wondrous magic to Christmas. TV historians and critics consider it among TZ's best.
Gerard