One of Douglas Adam’s “Hitchhiker’s” books posits a massive colony ship carrying all the survivors of a doomed planet to a new home-world. But a meteor collision dislodges the central computer core that contains the entirety of the alien races’ collective memories. The ship crashes on Pluto, the aliens emerge from suspended animation, but with no recollection of who they are or where they came from. With nothing else to base a society on, they pattern their lives after reruns of 1970s TV series that have reached Pluto.
On Earth, an intrepid reporter named Tricia (a parallel timeline version of Trillian) gets approached by a few of the aliens and invited to see their colony. Their spacecraft and houses are lined with shag carpets and tacky wallpaper. The aliens sit in barcalougners and watch TV. They eat McDonald’s food. When Tricia asks how they got “McDonald’s”, they respond “We stand in line for it.” “That” thinks Tricia “explains an awful lot.”
Tricia is returned to Earth despondent with the knowledge that she had a story that should have been the all-time greatest scoop in history - but she could have faked something that looked more convincing.
I remember an old Amazing Stories episode where some nerdy high school kids are building a TV antenna as a science project. The start out with simple things like getting better reception than rabbit ears, then signals from out of state, then across the world, and then pick up broadcasts from another planet.
Not entire sure how relevant this is, since the Enterprise is orbiting that alien planet while they watch its broadcasts. It’s not like they are watching the show from Earth or some other distant place. I think the same might be said of Arena, where the crew is allowed to watch the battle of Kirk and the Gorn.
For an episode where the Enterprise crew watch an alien broadcast from far away (although mostly in interplanetary space, not watching from near Earth), we have the two part episode The Menagerie.
Also, both Fred Hoyle’s “A is for Andromeda” and the film “Red Planet Mars” concern humans receiving radio messages from other planets, although not specifically entertainment broadcasts (as “The Sparrow” did.)
I believe there is at one episode of SG-1, wherein they broadcast a “space race” to multiple star systems.
(The memory is so vague. I may be thinking of Farscape)
In the novel and film Contact, SETI researchers are able to pick up a video broadcast signal interspersed throughout a stronger (audio?) signal broadcasting prime numbers. The broadcasts come from the direction of the star Vega.
The video signal is not alien entertainment, however – it is a re-broadcast of an Adolf Hitler speech that was (IIRC) one of the first television signals ever broadcast in real life that would have been strong enough to be picked up in outer space.