The puppets in the video are controlled by two people on is the head and the leg and then the other is the arms. All you really need is a large shirt or jacket then some dummy pants. The main puppeteer that is the head put their head through a slit in the back of the jacket and then hands go through two others and into the legs. For the arms the second puppeteer would stand behind the other and put his arms into slits at the top of the sleeves. At least that is how I envision it working.

I've never actually done it.
What you drew out would also work and is most likely more on par with what you see in the picture you just posted. I do imagine that in the picture though there are still two puppeteers. One is controlling the head and perhaps one arm while the other would control either the legs or the other arm. In this case I bet the arms and legs are manipulates with rods that are sticking straight back through slits. Snails idea about a stretch fabric that is pulled tight would help keep the slits closed up. In fact you might even want to put a hem in the slits and thread elastic through them. The puppeteer would need to be in black and you need a black background then also behind the puppeteer. In the videos I think they are actually inside a black out box of sort so no light comes in from above but you might not need to do that depending on how you set things up.