As K-pop acts take on increasingly ambitious performances at home and abroad, the people turning their music into a live spectacle are now stepping out from behind the scenes. Performance directors oversee nearly every visual element of a performance, from choreography and dancer formations to costumes, lighting and stage sets. Once largely seen as an extension of choreography in K-pop, the job is increasingly being recognized as a creative role of its own. That distinction has become visible enough to form an entire television competition. Mnet’s “Street World Fighter: Directors’ War,” which premiered Aug. 18, puts 10 established choreographers in competition not simply over who can create the best dance, but over who can best direct a complete performance. Instead of competing with their own dance crews, contestants vie to have their names credited as performance directors. The format reflects a distinction that has long been blurry in K-pop. Choreographers create the movements that make up a routine, while performance directors are tasked with deciding how those movements and