A rougly-similar lock is made by Simplex (now Kaba-Ilco) using five buttons. These have been around for a long time and you might some detailed information on the web. See also US patents 3,115,765 and 6,026,665. A further patent search for the newer ones like the image in your post might also yield some details but dealing with a patent search is a little more work.
Ultimately, the best understanding is probably achieved by taking one apart and seeing how it works.