If one uses 300ppi @ 11inches as the standard for a "retinal" display, 100ppi becomes retinal at 33 inches. I don't sit quite that far from my screen, though I suppose some people may.
And a couple other popular smartphones have been retinal at their typical usage distances for several months now.
Apparently 20/20 vision is defined as being able to distinguish things 1 arc-minute apart. This comes to 114 dpi at the 30 inches away that I just measured my screen at. And yet when I pick a small-but-generally-readable font, I can see that for example the leftmost leg of an 'm' looks different than the other two.
So I would say you want sufficiently high resolution that pixelization artifacts aren't visible, which means that adding or subtracting one pixel from a one-arc-minute item leaves it still at one-arc-minute. Maybe 2px/arc-minute would do this well enough, maybe it would take 3. But 1px/arc-minute still permits visible artifacts.
I need a diagram. I'll use the one on wikipedia's visual angle page.
At 11 inches, 1 inch has a visual angle of about 5.2 degrees. But the exact number doesn't much matter. You can set two instances of the visual angle equation equal (one for the unknown distance and one for the definition of retinal, an inch long at 11 inches distance), and simplify to give you what similar triangle ratios would too. A length, s=D/11, for the side of the similar triangle opposite the eye, which by the operating definition of "retinal" has 300pixels along it. So, we can use s as a scaling factor, 300ppi/(D/11)="ppi you need at distance D to be retinal". Solve for D instead if you wish.
That might not even be clear with the diagram, sorry.
And a couple other popular smartphones have been retinal at their typical usage distances for several months now.