Speaking only of feelings and impressions, (this is just my opinion) I've been unable to shake a feeling that BG may have been impersonating LE in some way.
IMO, in some of the earlier threads here, I read that the High Bridge was "technically" private property/off limits, but was also a popular attraction that people enjoyed while hiking/walking in that park. And, wasn't at least one of the girls admonished to keep away from that bridge (by her mom, iirc).
In the moment(s) after the video still was captured by the smartphone, I imagine BG producing some sort of fake ID (or badge, etc) while confronting the girls about their "illegal" activity. Then, he orders them "down the hill" and off the bridge, instead of ordering them back across the bridge, which may have further reinforced his ruse that the bridge was really "off limits."
It's possible he didn't need to brandish a weapon at that point in the scenario, expecting the girls to respect and obey an adult with a "badge." His tone of voice and delivery of those words: "Down the Hill" sounded authoritative and very serious to me, and I can certainly imagine why the girls would (at least initially) feel compelled to obey. IMO, IME