There's a ZIP of a registry file linked on that page that helps you reset the default back to Notepad and fix the issue. However, I don't want to reset the default, I want to keep Notepad++ as the default. So I modified the last bit of the file from
>>Re: No option for "new text document" after making Notepad my default txt editor.
Instead of messing directly with the Registry, have you tried using the "normal" way to set the OpenWith option?
Use Windows Explorer (or your favorite file management tool like XYplorer, Qdir, etc) to list any program with the relevant extension (e.g. ".txt")
Right click on the file (e.g. XYZ.txt), and select "Open With"
then select the "browse" option to find the relevant program (e.g. Notepad++.exe)
then check the box "Always use the selected program to open this kind of file"
then click OK
This should then allow you to verify you set it correctly by subsequently opening the file you selected with the program you selected.
(e.g. if you "right-clicked" on XYZ.txt, then when you click on "OK" it should immediately open XYZ.txt with Notepad++.exe)
If you want to see what happened in the registry when you did this, you can go to the registry and your change should be reflected by the addition of Notepad++ into the "OpenWith" list
There are also some freeware File Association "fixer" tools available for various versions of Windows. If you go that route, make sure the one you use is written for the OS you're using.