He knows more than he's letting on, but clearly he lacks any theory knowledge, thinking that an A is an A flat.
I think it's more like he grew up in a house with a piano, has never had a lesson, and at some point someone taught him I-V-vi-IV, and he's just done that every time he's found himself sat in front of the piano. So he's gradually gotten good enough to play through that chord progression reasonably confidently.
i.e. he has learned how to play the piano, albeit in a very limited way.
A better way to 'fake' playing the piano is to play using only the black keys - with good voicing and phrasing, it's easy to make it sound nice since it's just a basic pentatonic scale, which sounds pleasant to most people (though will sound a little 'oriental' to western ears). Takes a minute or two to learn to do that. That's much more "faking" it than what this guy is doing, which isn't something an absolute beginner could just pick up in a couple minutes.