It's a pretty short story. Not a "bad" basis for a movie, but the story seems to intentionally leave everything out about how this dystopian, alternate-universe America came about. I'm having a hard time imagining how you fill up a full length movie just watching kids walk till they can't and get shot for 90 minutes... Man vs Man story about human nature, but all of the unwritten background and mystery on how they came to this Long Walk is also kind of the point, and fleshing that out in a movie would change the whole meaning unless done very artfully...
The short story The Long Walk most certainly influenced it's full-novel, big brother, The Running Man.