How do headphones create spacial audio

Most people are familiar with surround sound, you place a bunch of speakers around you and when a speaker plays a sound it sounds like it's coming from that direction, because it is. That makes sense so why are some headphones that only have two speakers advertised as having spatial audio because of something called binaural sound. You can record binaural sound with a couple of ear shaped microphones. Makes sense right if you know what each ear would hear in a environment you could make it sound like you are in that environment. Check out this video from the verge for more about binaural audio https://youtu.be/Yd5i7TlpzCk and this one for 30 minutes in NYC https://youtu.be/2Gpl99s02Aw