Legality of publicly posting surveillance video of minors committing a crime?

One of my guilty pleasures is reading the "raves and rants" Facebook group for Central, where this community's exceptionally stupid come out to play.

Recently, someone shared a post from the Central Menchie's Facebook page, showing video of two kids stealing the tip jar (ages 10 and 12-ish). The father -- apparently not living with the kids, who are possibly being raised by their aunt -- jumped into the comment fray and threatened to sue Menchie's for illegally posting a video of minors in an attempt to identify them. He also threatened to sue some people who replied to his comments, claiming they infringed on his rights. It's all on the Menchie's Central Square Facebook page if you'd like to read the 250+ comments. The father really livened things up since he's old, trashy, and doesn't understand how internet arguments work. He alluded to wanting to IRL fight one of the commenters at Cane's Lemonade Day and demand an apology/free lemonade.

I know there are laws about photos/videos of minors, maybe varying by state and by intent. I'm curious whether posting the surveillance footage is actually illegal (the kids' names were never mentioned). Doesn't seem like it would be, and you'd think a responsible business owner would find out before posting the video, but from what I've gathered in other Menchies-related drama, the owner seems in over his head when it comes to managing his stores.

The thing is, these kids were almost immediately identified by the public because they're frequently spotted roaming around unsupervised. The police know who they are because they set some yarn on fire in the Central Walmart and caused a full evacuation a few weeks ago, and they stole a phone from someone in the hallmark store. No hope for those kids.