What is this kind of handshake called?

It's hard to tell from a still picture, but it looks like it's a "dap."

There are a lot of different types of dap. Some people consider bumping fists a "dap," but where I'm from, the fist bump is the least respectful type of dap (aside from a left-handed dap, which is basically an insult). The fist bump is the type of dap you give to someone whom you would call an acquaintance, but not a friend. It shows weariness and lack of trust.

A more common dap starts out like a handshake, but when your hand meets the other person's hand, rather than grasping and shaking their hand, you keep your hand flat and you each slide your hands back toward your body until only your fingers are touching, bending your fingers to make something that looks like this:

People will often keep their hands clasped like this and pull in for a one-arm hug at the same time. That looks like it might be what's about to happen in the picture you provided.

It's a pretty cool type of handshake since there are so many uses for it. I've seen my male friends dap each other as a greeting, a positive response to a joke or statement someone has just said, a quick way of saying "sorry bro"/"it's cool", a goodbye, etc