The speed limit does apply to cyclists, but that 20 mph sign was for a school zone and is only in effect when the lights are flashing, which they weren't.

I didn't see any other speed limit signs, so we have no way of knowing what the normal limit was (short of turning it into a game of Geoguessr), but my educated guess is that it's probably 35 mph. Edit: another commenter named the street and I found a speed limit sign for the opposite direction on Google Street View. It's 25 mph.