If it exists at all Dungeons & Dragons is probably pretty different - which of course would impact the development of roleplaying games generally, and through them Computer roleplaying games.
Not necessarily all that different. As the story goes, Gygax didn't like* LOTR, and only included hobbits, for example, becauseD&D came from combining medieval war-games with unconventional encounters, so it may well appear anyway, just with ogres instead of orcs, munchkins instead ofhobbitshalflings, etc.
he had players who did like it and insisted on their presence and availability.
Well, I guess it depends on how different you consider it to be without halflings, treants, balrog-like balors and Aragorn-ish rangers.
Meanwhile the D&D trolls and elves owed more to the ones created by - ALL TOGETHER NOW - Poul Anderson.
Seriously, I may misremember, but I recall pausing while reading The Broken Sword with the thought "Did he just
practically state elves have a 90% resistance to Charm and Sleep spells?".
And somewhere at the back of my mind is the claim that Gygax's personal preference was Barsoom...
Not to mention that some of the real icons come from cheap plastic toys eventually identified as bootleg knock-offs
of Ultraman monsters.
The question is whether D&D would have made it as big if there had been no Tolkien juggernaut, which I guess leads
back to the original, rephrased, question of how instrumental LOTR was for contemporary and later fantasy success.
*In fact, more reliable/confident/close sources may have used a stronger word.