My bet is that the option is grayed out, disabled, for some reason that does not have to do with the help topic; the poor sap who wrote that wasn't thinking about the possibility that the Remove-Hyperlink might be disabled because of .... because of .... well, because of some option that I can't think of just now.

By the way, I just tested it and you don't have to click-and-hold first to select the cell; you can just right-click straight on the cell, even if it's not the current selection, and it'll bring up the menu. And on my machine you don't have to do this one cell at a time; you can highlight a bunch of cells with hyperlinks in them, right click on the whole selected range and find Remove Hyperlink in the resulting menu. It works, too ... on my machine. But if it doesn't work for one cell on your machine, it probably won't work for many, either. The trick here is to figure out why you're not allowed to Remove Hyperlink just now. Is it an Options setting? Are you in the middle of running a macro? Are you in <F2> mode (whatever that's really supposed to be called)?

I googled "Excel Remove Hyperlink disabled" and found this. Does that fit your case?