How and why do they recapture like that with their hand?

Here is an example

https://www.youtube.com/watch?v=GL-uWmw4YMA

I would say it is a speed issues. Faster way to move and take the other piece off the board.

What do you mean? This looks normal to me. How do you capture?

They are extremely skilled!

What I always wonder is why pros play blitz with such shitty hollow plastic pieces. When they're unweighted, the pieces can go flying (as seen in just about every video where such a set is used).

I've never played blitz on such a cheap set in my life 

When they capture/recapture they pick up and put down a piece in one movement.

That's the cool way to do it, even in standard controls.

Yes, this is how most people capture as far as I know.

How do you capture? Do you use two hands or something?

The way I see it the natural way most people do it is a lot slower. Don't you remember when you first started chess it was different?

You can do that more slowly anyway.

Ok, I guess it's a matter of experience.

But in any case, the video you linked is a 3 minute vs 30 second game. If Carlsen captured slowly he would lose on time before move 20 lol.

Yeah, this is how I play in slow chess too. E.g. the thumb and first finger hold my piece while the rest of my hand lifts the piece to be captured.

Agdestein seems like a nice guy -- he had Magnus on the ropes 

Under what rule system and when? Using one hand is the right way and whether you remove the piece first then move your piece there or do it something like that doesn't really matter.