In the videogame "Middle-Earth: Shadow of War" the opening scene shows Talion, really Celebrimbor, forging a second Ring of Power to combat the original One Ring.
My question is whether this is completely made up for game purpose or if there is some obscure reference to it in some of the appendixes or anything of the sort.
Celebrimbor made three Rings of Power for the Elves (the three Elven Rings worn by Gandalf, Elrond and Galadriel at the time of the War of the Ring). However none of them was a second "One Ring to rule them all".
In those days the smiths of Ost-in-Edhil surpassed all that they had contrived before; and they took thought, and they made Rings of Power. But Sauron guided their labours, and he was aware of all that they did;
The Silmarillion: Of the Rings of Power and the Third Age
Page 287 (George Allen and Unwin 1977 hardback edition)
It's hard to prove a negative, but there is certainly nothing in the Appendix of The Lord of the Rings about a second One Ring. I don't recall reading any reference to such a thing in The Letters, or any of the books published by Christopher Tolkien.
If such a Ring had existed, Elrond would surely know about it, and it would have been discussed at the Council of Elrond. In fact this is all Elrond says about the forging of the Rings:
Then all listened while Elrond in his clear voice spoke of Sauron and the Rings of Power, and their forging in the Second Age of the world long ago. A part of his tale was known to some there, but the full tale to none, and many eyes were turned to Elrond in fear and wonder as he told of the Elven-smiths of Eregion and their friendship with Moria, and their eagerness for knowledge, by which Sauron ensnared them. For in that time he was not yet evil to behold, and they received his aid and grew mighty in craft, whereas he learned all their secrets, and betrayed them, and forged secretly in the Mountain of Fire the One Ring to be their master. But Celebrimbor was aware of him, and hid the Three which he had made; and there was war, and the land was laid waste, and the gate of Moria was shut.
The Lord of the Rings Book Two, Chapter 2: The Council of Elrond
Page 242 (Single volume 50th Anniversary Edition)
I have to conclude that this was made up only for the game.
The idea for a second One Ring may have come from Tolkien himself.
In the Forward to the Second Edition, Tolkien states that The Lord of the Rings is not an allegory for World War II or anything else for that matter. If he had wanted it to be a retelling of the war, it might have included:
Saruman, failing to get possession of the Ring, would in the confusion and treacheries of the time have found in Mordor the missing links in his own researches into Ring-lore, and before long he would have made a Great Ring of his own with which to challenge the self-styled Ruler of Middle-earth.
While it doesn't resemble the plot of the video game, it does provide the suggestion that there could be a second One Ring.
No
The idea of creating another ring in order to oppose it to the One Ring is alien to the way Tolkien built the world. See, one of the plot points of the Lord of the Rings is that the One Ring (designed to slave the other Rings) is defeated, not by a big army, but by a weak halfling. The army going to war against Mordor was just a decoy, they were sacrificing themselves hoping that Frodo could complete his mission.
A second character like Sauron or Saruman would indeed attempt to forge another Ring of power -if technically able- to fight force with force (and the Middle-Earth could end up enslaved by the bearer of this second ring instead of Sauron), but it's not how the white side behaved (despite all his limitations and sins).
