We've had forward-slash genres for a long time: before I joined the site, at any rate. Military/War predates me. So it's been around for at least the last 2-3 years. To the best of my knowledge, no one has mentioned confusion in that time.
Ditto for Automobiles/Vehicles, Cinema/Theatre, Cooking/Food, Design/Decorating, and... 9 more.
The only two forward-slash genres that were changed recently were Pets (into Animals/Pets) and Wildlife (into Outdoors/Wildlife). And Spy/Espionage was added.
We can change the / into a - or _. It's unlikely we're going to split out those genres, though. However, it seems odd that it's only causing problems now.
I don't claim to know much about API, but why are the digital video files using the genre name?