Well who more qualified to coin the term than Lloyd? But it's no good. "Epic stature" is just too vague.
Tolkien, or at least C. Tolkien, had a bit of a different idea. He (of course) divided high and low fantasy semi-linguistically (though, informally; it's not what he set out to do particularly, it just worked). I believe I read once that he had six different "forms" of speech -- you know, men of the southlands are brutes and drop their Gs or w/e, elves speak well, his pantheon of gods speak wellest, etc -- which he brought out for the relatively rare dialogue.
kleinbl00, if you do plan on reading LotR soon -- there are a million things I could say but I'll limit myself to this -- pay attention to the types of dialogue. How Sam speaks versus Elrond. How Frodo speaks versus the other hobbits. Everyone's different poetry. I would have loved to be forearmed with that knowledge the first time I read the trilogy. The Rohirrim speak slightly different "Westron" than do the men of Gondor. It's all very subtly woven so it doesn't disrupt your reading. Especially in Silmarillion, he often differentiates between classes or good/bad or dramatic/light/foolish by changing the speech patterns. Neat stuff.
Anyway yeah. High fantasy shouldn't probably be delineated by its content -- although that mostly works, it leads to something like this being labeled high fantasy. Problem is, that series is boring and the prose sounds like it came form a high school student. There's nothing "high" -- nothing elegant and royal -- about it. Because almost all modern fantasy authors are too damn lazy to worldbuild in that direction. They think a large map, 30 uniquely boring characters and a pointlessly complicated plot are what high fantasy is. They are idiots, and it's why modern fantasy is all but unreadable.
(And then there's Martin, whose books defy categorization. I think people have started using "realist fantasy" but that's an oxymoron and easy to confuse with "magical realism." And as you can see from Lloyd Alexander's definition, calling Martin's stuff "low fantasy" doesn't work either.)
EDIT: every time I get a badge I feel like I didn't really do as good a job as I could have. I feel pressured to do a classic compare and contrast, write a dissertation, bring other authors into my analysis, cite my sources. It's like r/askhistorians. I used to comment there and then it got too stressful.