Well, the video is not using toy puppets that's for sure... I don't get to see this show in my country, but from the looks of it (others correct me if I'm wrong), they're more 'muppets' with 'glove arms'. That is, the puppet has sleeves through which the puppeteers can put their arms; the hands of the puppet are really human hands gloved by the puppet's materials. It's likely there is one person operating the mouth and one of the hands, and another operating the second hand.

All you'd need for that is the right kind of puppet, a wall or something to hide behind (ie. the kitchen bench in the video) and the props/backdrop. You definitely can't achieve the same style by adding rods or something to the toys.

Are toys the only thing you can use? Perhaps you could get a proper puppet to do your filming with?

Good puppetry takes a lot of skill and learning.  There are no easy answers.

I understand....we are just looking for a possibility if what we want to do can be achieved with puppetry or not...
@ Na..we can surely use puppets..i believe we can always make puppets look like soft toys..

There's no doubt that you can do what you want with puppets - it's just that there are lots of different ways you can do it, and not all of them will suit your skill level/budget/time.

It may be that first you need to learn about how different styles of puppets work, and then find one that suits your needs. If you don't mind me saying, it kind of seems like you're doing the reverse (deciding on what you're going to do, then figuring out whether it will work), which isn't bad if you're a beginner but does make things hard when you actually come to make your film.

If you could get your hands on a good book about puppetry, it might help you understand how these things work from behind-the-scenes. The video you posted are the same techniques used in The Muppets/Sesame St - so I'm sure someone will have written about how it's done.