It's apt to compare Star Wars to Lord of the Rings rather than something like Star Trek, because Star Wars is fantasy and not science fiction, both stylistically and philosophically.
Tolkien, in his essay "On Fairy-Stories" outlines the basic philosophy of the genre as follows: to provide the reader with 1. recovery, 2. escape, and 3. moral consolation. Essentially, the purpose of fantasy is to offer the reader an uplifting hope for the good to triumph over the bad, both internally and externally, to provide the reader courage in an oftentimes ugly world. This is exactly what Star Wars does too, the original films at least.
To further elaborate on the video - Luke doesn't necessarily choose his own destiny so much as he chooses to embrace his destiny with honor and courage rather than fear and cowardice. His fate is not to save the world -- his fate is to become a Jedi, like his father before him. This means remembering and embodying all the good qualities of his father (=the dead) in himself (=the living). Luke never knew his father before his downfall, but he doesn't need to. He has ancestral memory. VERY pagan. Also close to some early expressions of Christianity, as well.
It feels timeless because it is. The Hero's Journey archetype has roots in pagan mythologies that have been around for thousands of years. European paganism, especially Germanic paganism, was essentially ancestral cult which dealt heavily with belief in fate and destiny. The original Luke Skywalker (as opposed to sequel Luke) is a pagan hero.
This is the purest form of the original message of Star Wars before its fatalistic worldview became stretched to implore cosmic ramifications with concepts like "the Will of the Force" and everything that entails.