There's many ways to avoid doing that and the electrician will prefer not to. Generally they prefer to route it laterally through the attic or basement and vertically in the walls. Sometimes, holes are cut in the wall to secure the wire or change its direction.
But if it must move laterally along some drywall and through all of the studs then yeah they'll need to open up that drywall to drill holes in all the studs.
I always thought this would make more sense to implement client side in the media player. But its probably easier to implement this way.