You'll notice they specifically mentioned commercial filming. Commercial speech has different protections under the Constitution as interpreted by SCOTUS (see Ohralik v. Ohio State Bar Association). Now I assume you're going to say that because bloggers are now repented as "the press" then your commercial speech is still not restricted. Fair enough but note time and place restrictions have been upheld by SCOTUS (see Ward v. Rock Against Racism and Clark v. Community for Creative Non-Violence) many times. You're not free to say whatever you want, whenever you want, wherever you want.

If you feel strongly that the law that officer was trying to uphold as part of his job is unconstitutional why didn't you let them arrest you and fight it all the way to the Supreme Court? That would certainly make for some interesting press. The fact that you didn't keep filming from the sidewalk leads me to think you are not convinced about that.

Almost every public park has limits on commercial activities for very good reasons. I wonder if that park rule was specifically about filming or just commercial activities in general. Regardless the time and place restrictions could still apply and make it a constitutional sound law.