The definition in the law even specifically excludes "Small, hand-held cameras shall not be considered remote sensing space system," i guess so that astronauts don't have to get a license 12 months before every mission. SpaceX cameras providing the video for the webcasts are certainly small and could be "handheld," so it seems to come down to the fact that no human is up there with them.
Remote sensing systems are a thing, and there are good reasons to regulate them. Tiny cameras stuck to the side of SpaceX rockets should not be classified as "remote sensing systems." When I think of remote sensing satellites, Landsat series and friends come to mind, not an off the shelf camera stuck on the side of a rocket.