The animated logo is just layers moving in 3D space with motion blur turned on. No Effects are added. There is no automatic one click solution.
After Effects is a layer based compositing program where each asset must be on a separate layer. Would it be difficult to recreate this animated logo? Not really, if you were familiar with the interface and knew about animating layers in 3D space. If you're brand new to AE then expect to spend quite a bit of time getting used to the interface and learning about keyframes, parenting, and AE cameras. You will start with a 2D solid as a background, shape layers for the shapes, and Text Layers for the text. You will position the text and shape layers in the final resting position, make them all 3D, add a null to control them all, then animate the Z position of each of the layers independently, then animate the position of the parent null to move the entire group, then turn on motion blur.
Here's how you get started with AE:Basic Workflow