There appear to be a number of "disconnects" of various types between the text and the game (even between the movies and the game).
To begin with, in the text there was never a garrison of Gondor stationed at the Black Gate. The Rangers of Ithilien patrolled a strip of land a few days' journey south of the Gate, just west of the Mountains of Shadow (the Ephel Dúath); but before Sauron "repossessed" Mordor, Gondor didn't have the manpower for such a guard, and afterwards, the Black Gate was far too dangerous to post a standing guard.
The Wikipedia article on the game describes the game's hero, Talion, as being "ritually sacrificed" by leaders of Mordor "in an attempt to summon the wraith of the Elf Lord Celebrimbor". In the text, Celebrimbor died in 1697 Second Age, some 3700 years before Sauron reoccupied Mordor; presumably (like that of any Elf) his feä or spirit returned to the Halls of Mandos in Valinor. Very few Elves returned from Mandos; and certainly none could be summoned in any way, nor could they appear as a wraith (it's not precisely clear to me what that means). Neither could Talion "return" or be "resurrected" in any sense; the Doom of Men required that when a human died, their feä went to the Halls of Mandos indeed, but then went on to some unknown place and never returned:
The sons of Men die indeed, and leave the world; wherefore they are called the Guests, or the Strangers. Death is their fate, the gift of Ilúvatar ...
(The Silmarillion, Chapter 1, "Of the Beginning of Days")
The one exception to this, Beren, was not truly an exception; Luthien was able to convince Mandos to let him return to Arda, but only for a brief time; Mandos had no power to keep the Gift, or Doom, of Men from him. Thus the situation in which Talion finds himself after death is incompatible with the world of Men as Tolkien described it, as is his encounter with Celebrimbor.
The article describes Celebrimbor, in the game, as having assisted Sauron in forging the One Ring and can wield the One Rings power. This is outright denied in the books, in which Sauron is described as forging the ring "secretly" (The Lord of the Rings, Book II, Chapter 2, "The Council of Elrond"). Celebrimbor is said in Appendix B to have "perceived" the designs of Sauron, an odd phrase if he was that involved with the Ring. It is also stated that the One Ring can only be wielded by Sauron and Sauron alone.
Again, there is said to be "a community of Gondorian outcasts living in Mordor". This seems unlikely: Appendix A states
At this time [about 1856 of the Third Age] it is thought that the Ringwraiths re-entered Mordor.
So the forces of Sauron had occupied the land for nearly 1200 years; and (given the time period, some time between 2941 and 3018), Sauron had recently reoccupied the land. It was not a healthy place for humans to be—Frodo comments, seeing two orcs fighting,
They hate us far more, altogether and all the time. If those two had seen us, they would have dropped all their quarrel until we were dead.
(Lord of the Rings, Book VI, Chapter 2, "The Land of Shadow")
Next, the issue of the "kingdom of Núrn": its queen, and her daughter, play important roles later in the game. There is no reference to such a kingdom anywhere in the text; Tolkien does, however, describe
the great slave-worked fields away south [of the plain of Gorgoroth] in this wide realm, beyond the fumes of the Mountain by the dark sad waters of Lake Nurnen.
(Lord of the Rings, Book VI, Chapter 2, "The Land of Shadow")
This "Lake Nurnen" is described on the map as the "Sea of Nurnen"; but clearly the same place is intended. There's no hint that the place is, or was, an independent kingdom at any point.
With respect to Gollum: Gollum did leave the Misty Mountains about 2944 (according to the timeline of Appendix B), and went off toward Dale; several years later (about 2951) he "turned towards Mordor". It appears to have taken him nearly 30 years (!!) to get there; the Appendix lists his acquaintance with Shelob, for example, as dating to about 2980. Gollum appears to have lurked around the borders of Mordor for another 30 years or so before being caught sometime between about 3010 and 3018. (This is one of the most difficult aspects of Tolkien's timeline for me to swallow; but I'll accept it for the purposes of the question.) So it would be possible, in theory, for Talion to have met Gollum; but as far as "leading Celebrimbor to relics of his past", as the Wikipedia article mentions, that assumes far too much knowledge on the part of Gollum—as well as assuming that these relics somehow made their way from Eregion (where Celebrimbor lived) to Mordor.
Most egregiously (in my opinion): Every time that Tolkien gives a story of a character who becomes enamored of power or revenge (as Talion does), the story is a tragic one and the desire for power or revenge is the tragic flaw (Túrin Turambar is a classic example; or Fëanor). This story, though perhaps it doesn't quite end here (as one would expect it leaves room for a sequel) should, if Tolkien's pattern is followed, end with the downfall of Talion. As it does not, it seems to display a fundamental misunderstanding of Tolkien's view of good, evil, and power.
One final note, unrelated but perhaps interesting: Although I don't know what "Talion" means, or is intended to mean, in Elvish (presumably Sindarin), I do know that it appears related to a Latin word. The lex talionis, or (more or less literally) "Law of the Same Thing", referred to the Old Testament principle of "An eye for an eye, a tooth for a tooth"—disturbingly relevant to a character whose purpose in life, or unlife, has become taking revenge.