I nearly perfectly duplicated the background graphic using a null as the parent for a few shape layers with some set matte and track mattes applied. The comp looks like this:
Here's the project file. Took me about 15 minutes. Used your sample video as a guide. The moving L is nothing more than a path animation with some matting. Not perfect, but the transform is only a couple of frames and it looks the same. If it were my design I would not bother and I would have made the initial graphics all in Illustrator and only converted the layer with the animated dashed line to a shape layer in AE. I've done hundreds of this kind of animated graphics and simple is usually better.