It isn't running at 1080p. It's doing "@2x" pixel rendering (commonly called "Retina") - so it uses 4 physical pixels to render one "screen" pixel, giving you much crisper.. everything.
It is not more pixelated. It's like scaling up all fonts and widgets by 2x, but still rendering them at 4k. So, the fonts and widgets are retina-sharp. Imagine using 4k as the resolution, but rendering all 14pt fonts as 28pt.
Though I get why you might think it's pixelated from stephenr's description.