Yes—output sharpening is ideally matched to the final viewing medium. In practice, that means resize for the target display first, then apply output sharpening appropriate to that output. Different destinations (screen vs print, larger vs smaller rendered image) can benefit from different sharpening.

For high-DPI vs standard displays, the main difference is usually the delivered pixel dimensions and viewing conditions, not that one needs a radically different manual sharpening method. If you export separate versions for different screen sizes/densities, each version should be resized and sharpened for its own target. Tools like Lightroom’s export sharpening are designed to do this automatically when you choose the output size and screen sharpening.

That said, several photographers would question whether maintaining separate retina/non-retina sharpening workflows is worth the effort. For many viewers, the visible benefit is small, and factors like display calibration, viewing distance, and whether people can actually perceive the difference may matter more.

So: for best technical quality, use output-specific resizing and sharpening; for practical workflow, one good screen export is often enough.