Please read the cited article by Fraser et al.
"... the practice of using the terms 'dpi' (dots per inch) and 'ppi' (pixels per inch) interchangeably inevitably leads to confusion, because dots and pixels are distinct entities with different properties."
I've got signed copies of all of Fraser's books, he of course isn't wrong, nor is Jeff. Jeff clearly differentiates PPI from DPI in the article when speaking of images composed of pixels and devices that produce dots (in this case, printers). If you or others are confused, I'm sorry.
The output of a high quality inkjet may appear continuous
Of course it can and thus, how is it NOT continuous tone?
but if you look at the print under a microscope you see innumerable randomly spaced color dots.
And when I examine a silver print with a microscope, I see grain. So what? BOTH appear without as
continuous tone. My B&W laser printer of a photo without a microscope, no, it does not.
You stated:
"A continuous-tone device such as a monitor ...." Really, even when examined with a microscope? Please explain how a display IS continuous-tone but an ink jet without either being examined with a microscope isn't continuous-tone. Because if the topic is confusion, you've confused me.....