Just to be clear, are you asking how to get the charcater to face the direction of the camera in third person? Your question is not very specific.
You could do something like this:
HumanoidRootPart.CFrame = CFrame.new(
HumanoidRootPart.Position + (Camera.CFrame.LookVector * Vector3.new(1, 0, 1))
This will make the HumanoidRootPart face the same direction as the camera, but only on the X and Z axis.
The effect will be instantaneous, so you should research TweenService or cframe interpolation if you want non-instantaneous and more natural rotation.
Edit: In the video, it actually looks like only the waist joint is being manipulated, rather than the position of the entire character. In which case, you can implement something like this (for an R15 character):
local player = game.Players.LocalPlayer
local character = player.Character or player.CharacterAdded:Wait()
local HumanoidRootPart = character:WaitForChild("HumanoidRootPart")
local UpperTorso = character:WaitForChild("UpperTorso")
local WaistJoint = UpperTorso:WaitForChild("Waist")
local WaistC0 = CFrame.new(0, 0.2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1)
local Camera = workspace.CurrentCamera
local angle = math.asin(Camera.CFrame.LookVector.X) * 0.8
WaistJoint.C0 = WaistC0 * CFrame.fromEulerAnglesXYZ(0, -angle, 0)
You can do similar for the neck joint to rotate the head.
More reference material about CFrames: