How they did it? (3D-like screenshots with animation)
This looks like 2.5D to me, probably in After Effects. You create high res art, perhaps by capturing web pages from a 4K display, then animate each screen. Its only a small amount of mousing. Then use the After Effects 3D camera to spin objects and place them in a depth field. turn on Motion Blur and add shallow DOF with a defocus effect driven by depth.