I hadn’t seen the first LOTR since the film came out in 2001—but I was able to find the beginning on YouTube. Here it is:
Yes, this is a prologue. It “tells some earlier story and connects it to the main story.” Other examples are the beginning of Despicable Me, and the opening sequences of many Bond films.
At the same time, the LOTR 1 prologue illustrates an additional technique as well. It is primarily voice-over, spoken-word exposition. Voice-over exposition can be used anywhere in a film. One must be cautious about using it, as often it can be more fun for the audience to discover this information during the story, rather than having to absorb it suddenly all at once. But as shown by this page on letterboxd.com, which lists a variety of films that use this approach, it a technique that has often been used very successfully.
So yes, the beginning of LOTR 1 is a prologue. Prologues are a great way to introduce your main character and his or her world before your main story begins.