No problem at all. I can't watch the video you posted with sound, but the cat in it seems to have adapted very well. He runs very fast in front of his owner in the yard, with his tail curled to the side like mine do when they are playing.
That is a happy/excited sign. There are two stressed cats at the very end, but the reason for the creeping and crawling is because they are facing off. See how the ears are laid flat, fur is erect, and movements are slow with a fixed stare? That is two cats having a dispute, and they do that no matter the leg number.
.
The very first clip of him in the yard looks to me like he is purposefully moving stealthily, either to stalk or to not be seen by something else. You can see where he speeds up when close to the bush/cover.
You're very welcome, glad they helped give an idea on what the typical process is like.