The switch on the side of the iPhone shouldn’t be used for muting entire applications. While the phone is on silent mode with the switch engaged, apps should still play sounds for things like audio and video (see: all of apple’s apps, and everybody else’s apps: youtube, downcast, facebook, MLB, Hulu, Netflix, HBO Go, et. al).
Currently, with the switch engaged and the phone on silent, playing a YouTube video inside the app plays no audio until the switch is disengaged.