Take a look at one of the older dockets on the case and decide for yourself what they're saying:
https://docs.justia.com/cases/federal/district-courts/missou...
Page 14, sections 4, 5, 6, and 7 are the incidents relevant to filming.
With respect to section 5, Akins filmed in the lobby, was asked to stop, and the person who asked him to stop was told that he was in the wrong for saying so. Section 6, he wasn't allowed into a media event because there wasn't a ton of space and he didn't have credentials. Section 7, he was posting video to the PD's and the city's Facebook pages and they removed the videos.
These are discussed on page 34, last paragraph. Seems like Akins is more interested in retaliation charges, and that's what the court is addressing here. The "he has no constitutional right to videotape any public proceedings he wishes to" seems a bit out of place as I re-read it, but I guess it's just establishing a baseline? I'm not sure what specifically the statement is meant to respond to.
The only thing that seems like public proceeding is the media event, and so in that context the judge is saying that I can't just bust in with a smartphone and say I have a constitutional right to record the event.