I can't see anything in the video. When was the last time you added something wet (coral/rock/fish/inverts) to the tank? Did you QT it?
Most likely Ich, some people just live with it in their tanks and move on.. sometimes the ich gets too bad and wipes out the tank though. It can depend on species, example, I had a powder blue tang that was badly infected and died, but no other fish even showed spots.
There are a couple of other things that appear as white spots.. next one up would be velvet which you have to treat or you'll lose fish, all fish need to be removed and treated with Chloroquine Phosphate if it's velvet. It's also effective against ich.
There is no reef safe treatment for either parasite... and removing only fish showing signs now wont help, as the tank is still infected, you'll need your tank to be without fish for 72-90+ days if it's ich, the longer the more likely it will have all died out.