>And so these Photoshop files (PSD) have the Pantone colors in the file data, not just the RGB values?

Yes. For example, if you used Pantone 289 (a dark blue) in your file, Photoshop embeds that color as a separate color “channel” in the file.

>So then when you display the file, it has to map to the color system the computer users? Is that accurate?

Also correct. The PMS 289 blue has a corresponding RGB (almost all computer displays use red, green, and blue pixels) color “break”. The “break” tells the computer what color components most closely match PMS 289.

>At this point, do you expect an "open standard" to replace Pantone or is there just too much investment?

That’s a really tough question. Businesses have been using and paying for Pantone for literal decades. There is a ton of work involved in making colors match across screen, print, textiles, paint, apparel, cosmetics, and architectural (and I’m sure more). Replacing that would take a tremendous amount of work. There are open alternatives, but they don’t have the breadth of industry solutions that Pantone does. The ability to pick a color and have it look the same on screen, in print, and on a dress isn’t easily replicated.

IMO, Adobe and Pantone will solve this stalemate, or businesses will get used to paying for Pantone directly. Small users who’s don’t want to pay will simply get by with “close enough” or alternatives that only work for screen and print, which is the most common use case by far.