You need to think about pixel density instead of resolution.
A 1080 video is 1920x1080 little blocks of visual goodness. But that says nothing about the size of those blocks; they could be teensy on your iPhone, or 1 foot tall on a stadium monitor. But the image resolution is still 1920x1080.
An iPhone may have 401 pixels per in (!! on an iPhone+). The riMac is 218 PPI. An old iMac is 109 PPI.
If that 1080 image is shown on any of those screens with one pixel in the image mapped to one pixel on the screen, the video will be different sizes, since the individual pixels are different sizes. With more PPI the pixels are smaller so 1080 of 'em will fit in a smaller space.
Below I have a picture from a digital camera; note how it's bigger on the 2560x1440 screen to the left, and smaller on the riMac to the right. That's because each pixel of the image is displayed with a smaller pixel on the riMac than the old iMac.
But note that this would be bummer for say text; it would be ½ as big on the riMac. So retina awareness means that the developer makes an icon with twice as many pixels in the IMAGE of the icon, so it can be show 2x as big on the riMac, which makes it equal in size to the old iMac's display of that icon. Or text. But some applications know that you wanna see pixel for pixel, not doubled, on things like images. Like Aperture; that's what you see in the photo. It knows I wanna look at my images in FULL. But not all applications are that aware; Preview, e.g., will show an image the same size on both riMac and iMac, which means that on the riMac it is blown up 2x. Oh no, some say.
But remember what's really going on, that the image pixels are independent of the screen pixel size. So when an image is doubled on an riMac what is occurring is that an image pixel is mapped to four riMac screen pixels. But those four pixels are still as small as a regular iMac pixel. So you probably won't be able to see the difference. It's like taking one pixel of the iMac screen and chopping it up into four with the same color; little change. Of course that means that some sharpness is left on the table, but that's because the 1080 image only has so much info; it was a 5k image it would be able to fill those littler pixels on the riMac.
Or, in short, it's kinda like watching SD television on your HDTV. It looks crappy, but that's because the IMAGE is crappy, not the screen. Your HDTV could show it at pixel for pixel, and it would be much smaller, and might seem sorta sharper, in the same way that moving a TV across the room makes it seem sorta sharper cuz you can't see the pixels. You can replicate that effect by reducing the size of any object on any screen. That's the retina effect: the idea is that you see an image without pixels at some particular distance; for the iMac that can be 32", the riMac 16". Front row of theater vs back row.
HTH.
