Martial arts movies aren't usually known for their gripping stories, but a rare few of them can break the mold of the genre with genuinely fantastic narratives alongside gripping action. For the most part, martial arts movies are given a lot of leeway when it comes to their stories, with gripping hand-to-hand fight scenes being the primary draw for audiences of the genre. That being said, some of the best fight scenes in martial arts movie history come from films with brilliant narratives that compliment the action.
Martial arts movies with earnestly great stories come in multiple varieties. Often, the period setting of martial arts films allows for some fascinating political and cultural drama sprouting from the relevant movements or historical events of the time they take place in. In other cases, lovingly choreographed action is used as an emotional vessel for two characters to hash out their relationship, mirroring the intimacy of other areas in life with the intimacy of combat.
Exactly! Ghost Dog in particular could fit perfectly in that, and boxing is a martial art.