In general, this expression is commonly used because it is a useful way of defining a space that begins with any upward-facing surface and extends towards the sky.
I spent the autumn days glowering at the leaves on and above my lawn.
As far as this specific instance goes, we can tell from the remainder of your example sentence's paragraph what the author is referring to:
But foreign policy statements are made all the time on and above the sidewalks of New York. That explains why street corners are named for the likes of Nelson and Winnie Mandela of South Africa, the assassinated Yitzhak Rabin of Israel, the murdered Kudirat Abiola of Nigeria and the Cuban exile group Brothers to the Rescue.
This use of the phrase covers locations of memorial plaques and street signs, as well as the contentious Empire State Building lights that are the subject of the article. It's possible that there are metaphorical implications as well, related to the people on the sidewalks and in the buildings “above” the sidewalk, but the literal meaning is at least clear from the rest of the paragraph.
Named street corner, above the street:
Memorial plaque, on the street: