Story Beats are a storytelling principal that have a very heavy impact on a story being satisfying to read, watch, or hear, specifically related to pacing. An action genre story needs to have things happen more frequently than a Drama or a romance.
Hitting a similar Story Beat rythm and having the same KINDS of beats will assist in providing the right atmosphere/feel. Rules that help do that are better than ones which prevent it. D&D doesn't feel much like an action movie, because the pace of combat is very slow. Combat in Apocalypse World feels a lot more high-octane because it's much faster, and more stuff happens in a shorter period of time. So when desiring an action-movie feel to combat, AW-based systems have an edge over D&D-based systems.
D&D feels like really complicated chess or a very small-scale wargame, because that's basically what the combat is. There is a reason why the D&D miniatures wargame was a natural extension of D&D combat with little by way of problems.
In short, Story Beats means "genre-based pacing" or it means "the important stuff that happens in this genre." Both are acceptable. A system that helps with those two is good. One that does not is not as good.