Seems to me that the question here is turning on two points:
1)
Stylistic: to write
like Tolkien in the sense that the story is an amalgam of contemporary novelistic realism and Romance.
2)
Thematic: to write about the same kind of world or world-view as Tolkien did, in the sense that the story is an amalgam of contemporary beliefs, ideals and more archaic ones including Romance (but, I think, more forcefully Anglo-Saxon ideals).
In my own humble opinion, very few writers before or after Tolkien have been able to pull off both of these very tricky balancing acts as well as the professor...but I shall avoid "gushing" (!

!) For my own tastes, fantasy that does both at the same time is the most pleasurable for me to read. But there are other finely crafted and engaging fantasy tales that do one or the other, or which priviledge one over the other.
Le Guin's
A Wizard of Earthsea is a story in which contemporary values and beliefs about race, gender, existential philosophy and psychology are fully at the front of consideration, but it is told in a consciously archaic mode with a narrator reminiscent of folk-tale and all the motifs of fairy-tale and mytho-heroic quests.
Stephen R. Donaldson's Thomas Covenant series are written in an entirely contemporary fashion with no sign of archaism in the narrative style (that I can see) but it presents a world governed by a more remote and distant set of values which are presented as the key to curing the "disease" of modernity: disbelief.
Both of these works were and are hailed by critics and audiences as being in the "spirit" or "tradition" of Tolkien, which is I think legitimate. Like Tolkien they work with this mix of contemporary and archaic in both style and theme, only they do so in slightly altered form in terms of that mixture.
Back to lurking.