Clicking "Apply styles" again, and then "Modify" shows that the "Do not check spelling or grammar" checkbox is still filled-in-selected.
In other words, the language setting didn't "take".
This is what I remember that I used to be able to do with older versions of Word. For some reason, I can't get it to work now.
OK, I figured it out on my own.
The quoted section was the clue. The "Do not check" setting was indeterminate. It's also the case that the selection of the language was indeterminate! The "English" language was not selected. Selecting "English" allowed the "Do not check" setting to "take".