I didn't see anything that would require the use of third-party plugins. Most of the effects looked to be simple wipes, linear & radial(Transitions). The lines looked to be paths with a stroke(Generate) applied to them. Though if I were to do that I would probably use shape layers, little more control.
Is your 4th picture, are you talking about the blur? That looks to be a simple motion blur, you move a layer, turn on motion blur for that layer and turn on motion blur for the composition.
Also, it's helps a bit more to tell us the timecode of the effect from your video, since it's motion graphics, it's easier to see it in motion.
"I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work."
---THOMAS EDISON on inventing the light bulb.