Walking like that is only something I ever do when being instructed to march by shouty people, who then proceed to get unbelievably pissed off about it. This is not intentional and I find it very hard to end up doing this in any other circumstances, it just seems like my subconscious enjoys causing me shit.

I tried to do it; walking was possible with a weird sway of the upper body, while running is impossible.

Running is totally possible! Perhaps it just takes a bit of practice. It's involves a lot of awkward lurching.

Try not moving the torso at all, and keep your hands in front of your thighs. Simply flip your palm up and slightly forwards when you want that leg to move forwards, It's called Namba Aruki in japan.