I know you don't actually want to hear from me, but I waited a day and nobody else tried to help, so...
Kenny's method is not exactly ideal for a couple reasons:
1) RMS is not the same as LUFS. There are important differences in the way they are calculated. It's often "close enough" with normalish music as a source, and will probably work fine if you're just "eyeballing for YouTube", but if you really have to meet a LUFS standard, you should really measure LUFS;
B) I'm pretty sure all of those streaming services are looking at the "Integrated Loudness", but the method in the vid can only measure "Short Term". And yes, Kenny seems to be cross-comparing reaper's short term against the plugin's integrated LUFS. This matters most in very dynamic material. On rock song that just gets loud and stays loud, the two numbers will probably close, but if you've got a gentle intro and mellow verse and then a big climactic chorus, what you see on reaper's meter will depend on what part of the song you're playing. Worse, the integrated value can't be expected to match any of your short-term readings except by accident. Like, if you measure the loudest point, you might turn it down more than it needs to be, but if you measure the quietest part, YouTube will end up turning it down for you.
But the ultimate answer is (as almost always) that it depends on what you're trying to do. If you're really trying to play the Price Is Right (as close as possible without going over) in order to deliver a product to tightly specified standards - like a TV show for broadcast, use SWS or some other method to get real integrated LUFS.
If you're really just trying to get it "right" for streaming media, Kenny's method will definitely get you close enough. I use a very similar method (with a slightly larger RMS time) for most of the things I do. Its the way I've always done since my first analog recordings 30 years ago.
If OTOH, you're actually trying to extrapolate from this to "gain staging" on individual items or tracks, the answer is pretty much "yeah, that's exactly what those meters are for".
I really do hope that some of this helps.