This sequence serves to introduce the puppies as individuals, though only four of them get named. Patch, Lucky, Roly and Penny get bits of business to separate them out of the pack.
The dogs are just like the audience for this film: parents and children together watching entertainment on a screen. The children are emotionally involved with what they're watching while the parents are somewhat jaded. What's most important is the easy relationship between the parents and children, content to spend time together and enjoy each other's company. The comedy is gentle, but based on observation of real family interaction.
What's on TV is a satire of 1950's fare. Westerns dominated TV in the '50s, as did old B westerns and serials. Given the cliffhanger ending of the Thunderbolt episode, it suggests that the footage was from an old serial. Thunderbolt himself is based on Rin Tin Tin, an actual dog brought home from Europe by an American soldier in World War I who went on to be a very popular Warner Bros. star in the 1920s. In the 1950s, Rin Tin Tin was a TV series (not starring the original dog), as was Lassie, both shows that the 1961 audience for 101 Dalmatians would have been familiar with.
This sequence is an example of why I object to the mystique of the nine old men. Eric Larson is the only one of the nine present in this sequence and he gets several personality close-ups. Hal King does about as much footage as Larson, yet King is a non-entity in terms of Disney history. King started at the studio in 1936 and animated on every feature from The Three Caballeros (1945) to Robin Hood (1973), yet who has heard of him? A quick scan of my bookshelf reveals that he animated some of Michael in Peter Pan and worked on the soccer game in Bedknobs and Broomsticks, but that's not a lot of recognition for a 37 year career at Disney.
I see nothing about King's work in this sequence to rate it any less highly than Larson's. Larson does some great work on scenes with Patch, but they're no better than King's scenes with Roly. The animators' work blends together without a problem and King gets some nice close-ups with Pepper (named only in the draft, not on screen), sitting on Pongo's head in shots 6, 24, 32 and 42. King captures the fleshy nature of dogs with the distortion in Pongo's brows and from an acting standpoint shows how involved Pepper is with the TV show while Pongo is clearly taking more pleasure from his children's reactions than he is to the show itself.
Art Stevens and Julius Svendsen do the animation on the TV. It's meant to be melodramatically over the top and they succeed in hitting the right tone. I assume that one of them did the Kanine Krunchies commercial, a parody of the UPA-style of commercials of the time. While it's a parody, it's better animated than many '50s commercials.
This sequence serves to create identification between the family on screen and the families in the audience. The quietness of this sequence serves as a rest between the excitement of the puppies being born and the kidnapping to follow. Once the kidnapping occurs, the peace that this sequence represents will be shattered until the film's finale.