There's no knowing for sure in stuff like this. I can't say anything about role playing games but as for Tolkien:
1. The LR is a written work meant to be read. Tolkien takes you slowly from a more familiar setting (derived from rural England) which he describes in a familiar style, to more ancient and higher realms, gradually shifting his style and tone to a higher and more serious level, using archaic terms like "fell." The transition is so gradual and well done that one doesn't notice, it all seems "right." Also there are always our semi-modern referants, the Hobbits, around to put things in perspective, make the high action accessible.
2. Shakespeare wrote plays that were meant to be watched. Reading him can get one lost fast: the archaic (to us) language hits us at once, everything is conveyed by dialog (there are few stage directions, descripions of setting, etc.) To kindle an interest in Shakespeare, take a kid to see the plays, especially an eerie action packed one like "Macbeth." Even so, be prepared to be lost initially: I always am, because I try to get oriented by paying meticulous attention to the words. When I rekax and let the word and action "wash over me," I get into the spirit of the play much faster.
3. Orientation: WS lived during the transition from traditional to modern times, he is full of allusions to traditional practices and images, but he is critical of them. JRRT is a highly critical modern, who it seems thought that we'd be better off if more traditional ways were still guiding our lives.
4. JRRT himself was critical of Shakespeare, especially his treatment of elves (blaming WS for much of our popular image of elves as tiny winged creatures) and of Macbeth. He was sorely disappointed when the prophecy "Birnam wood to high Dunsinane," that is a forest marching on a fortress, turned out to be human soldiers holding branches as camoulflage. Shabby he called it, and corrected things in the LR when the ents marched on Isengard.
5. While ignorant of role playing games, I'd say that they seem to emphasize strategy over speechifying. Thus, while they won't help a kid see through the poetry to the actions it describes, they may help see the intricacies of various schemes the more plotting characters (Iago, for instance) carry out. Bear in mind that, in WS, many critical actions take place off stage, to be described after by characters.

Good luck.