Apparently, this script doesn't work with Firefox (tested against Greasemonkey and Tampermonkey)
I've briefly skimmed over the script syntax and I don't see anything right away that would prevent it from working. Do you get any errors/warnings in Browser Console specific to the script?
However, since Firefox has dropped RSS ...
Never utilized that feature however I do briefly check in Firefox (Fx) the XML generated before importing into Thunderbird's (TB) feeds which definitely supports RSS and atom feeds (and obviously not a Userscript engine there).
... on Falkon
Btw what version of Falkon are you using please. I loaded in their latest under Linux and there is no GreaseMonkey (last known properly casing) extension via their snap but is present via current distro (which is older). As the AM of the site it is on my lengthy TODO list to verify the on-site documents.
I suppose I could fire up a VM of Windows and check that in a bit but anyone attempting to diagnose your question would need to know to compare.
I'm using Falkon Browser which has it's own Greasemonkey extension.
I'm happily using Newspaper Native Feed Reader on Falkon.
Apparently, this script doesn't work with Firefox (tested against Greasemonkey and Tampermonkey).
However, since Firefox has dropped RSS (why, I don't know) we can still open files with PHP and XML extensions (in contrast .atom and .rss open download prompt since 2018), so trying against these feeds doesn't yield results.
It might has to do with these:
http://camendesign.com/blog/rss_is_dying (RSS lives on!)