Coastal storm drains let out directly into the ocean, bay, gulf, or whatever the water is that makes it a coastal area. A tidal surge or severe wave action can run backwards into the storm drain system.
The pictures below show the street one block closer to the water than where my house sits during the highest surge we experienced here from Hurricane Dennis. The water is salt water from the bay which came up through the storm drains. This was a softer, gentler version of what probably happened in the video.
Edit: Found a site that says it's on I-35W In Minneapolis. That makes it not coastal, huh? But they supposedly had 8 inches of rain in a 24-hour period during the storms of July 3-5.