Funny anecdote, the Telstar satellite had an earth station in Andover, Maine, as it was accessible to phone lines but far from terrestrial interference. It had such an impact on the town they named their school "Telstar High School."
Then the "birds" were sold and renamed "Intelsat Americas" which doesn't have the same cachet.
The Wikipedia page on the Telstar satellite mentions the Andover station, the other end was Goonhilly Downs in southwestern England. And it looks like they still call it "Telstar High School", Bethel, ME.
The rocket shown in the video appears authentic, a Thor-Delta.
When I was very young, I remember my older brother calling us outside to watch a fast moving star in the sky. It was the Echo satellite, a precursor to Telstar.
This song always touches an emotional chord for me. To me it resonates with the innocent and unbridled faith in technology that was the '50s and early '60s. A faith that has been tempered over time.