That's a great question. It's a mixture of technical skill and intellectual depth.
For example, throughout Scotland placenames are a mixture of old Gaelic, modern Gaelic and Norse, and then there are the Anglicised versions on top. So learning what placenames mean is something I did in school and it's a fascinating subject.
So when Gildor is talking with Frodo, and mentions the "...Branduin, that you call the Brandywine..." (quote from memory; might not be correct), that's exactly what happens with placenames. It's that level of depth (in all aspects, this is just an example) that makes it a great work. You can read more on just the name of a river at https://tolkiengateway.net/wiki/Baranduin
Enjoyment of art is, as you say, totally subjective, but anyone who's artistic can generally identify when something is a great work even if they don't personally like it.
Everything has shortcomings but as a work of literature lotr is very obviously a great artistic work and the fact that you don't know that tells me immediately that you've never produced anything worthwhile.
What makes LotR a "great artistic work"? What makes Stardew Valley not a "great artistic work"?
Just like some books, films, or other art can resonate and have a profound impact on a person, so can video games.