Others with more knowledge than I would have to answer your question. I checked your link and studied your images and I am not sure if you are taking in to account the way monitor screens interpret/present the information they are displaying to the viewer. I apologies if that come across wrong and is oversimplifying the conundrum.
If you zoom in on any diagonal line (or circular line) you will always see a 'staggered' line - as in your zoomed angles image - because the screens can not replicate a line as you or I would draw it with a pencil or pen. That is because of the PPI resolution of the screen - to me anyway - made up of squares, that's how I interpret and understand it.
I've always understood monitor screens to be made up of X number of squares depending on the resolution it is set at. The more you zoom in the more 'pixilated' the image becomes and is seen on diagonal lines.
About 18 years ago I had to edit an image scanned from a photograph - taken of a line drawing in a book. The image was of a bird in flight around a bush/tree. I only wanted the image of the bird so had to remove all the rest around it. I had to zoom in considerably to get as fine a detail as I could and had all these jagged edges for the bird; wings, tail, head... made up of squares. I did not have to rotate any part of the original 'digital' image.
Maybe I'm misunderstanding you and the question of an image becoming 'lossy' if/when you do any rotation at an angle but I can only express what my experience on 'manipulation' of images has shown me. So I apologies again if I've misunderstood the question you want an answer to