I interpret the Warrior of the gods (hereinafter WoG) the description refers explicitly to the part of the resurrection of the spell, and not necessarily the fact that the spell does additional things. I interpret WoG in this way, since Raise Dead is used as an example. Raise Dead has additional effects, but we can reason that make Qualify for the cost exemption because it is included as an example. Therefore, these additional effects should not matter to WoG, so the only thing that remains is that should Matter is the resurrection itself.
Clone also does additional things (creating the body, in this case), but that is not what disqualifies him. The clone does not qualify for the cost exemption because it transfers the soul of the creature to a new body, instead of resuscitating it. This is supported by the answer to the question you linked in your comment.
This leaves us with 4 spells that we can focus on:
Revive, reincarnate, resurrection and true resurrection.
There is also one more spell that is capable of returning a creature to life: Desire. If we were concerned about the material costs for Wish (which we are not), we would treat Wish in a similar way to how I describe True Resurrection below. Whether or not this spell would do qualifying for a cost exemption would depend solely on the content of the desire in question, and not on the description of the spell, according to my previous interpretation. However, this does not matter ultimately, since Wish does not require components of material to mold.
That said, let's examine the remaining 4 spells on our list:
The description of Revivify says:
You touch a creature that has died at the last minute. That creature comes back to life with 1 hit point. This spell can not bring back to life a creature that has died of old age, nor can it restore the missing parts of its body.
This is simple enough for us to reasonably reason that this spell qualifies for the exemption.
This spell comes with attached strings (emphasis mine):
You play a dead humanoid or a piece of a dead humanoid. As long as the creature has died no more than 10 days, the spell forms a new adult body for him and then calls the soul to enter that body. If the soul of the target is not free or unwilling to do so, the spell fails.
Magic forms a new body for the creature to inhabit …
This spell is read similar to Clone, so we can consider that this spell does not qualify for the exemption. We are forming a new body here, as we did with Clone.
The spell of the Resurrection reads similarly to Raise Dead:
You touch a dead creature that has been dead for more than a century, who did not die in old age, and that is not an undead. If your soul is free and willing, the goal comes back to life with all its hit points.
This spell neutralizes any poison and heals the normal diseases that afflict the creature when it dies. However, it does not eliminate magical diseases, curses and the like; If such effects are not eliminated before casting the spell, they afflict the target upon returning to life.
This spell closes all mortal wounds and restores the missing parts of the body.
Returning from the dead is a test. The target has a -4 penalty on all attack rolls, saving shots and skill checks. Each time the target finishes a long rest, the penalty is reduced by 1 until it disappears …
If we can reason from WoG's description that Raise Dead works as written, we can also reason that Resurrection should qualify. The important difference between the spells is the effective time frame.
The true resurrection blurs the line between Clonar and Elevate Dead (the emphasis is mine):
You touch a creature that has been dead for more than 200 years and died for any reason, except old age. If the soul of the creature is free and willing, the creature comes back to life with all its hit points.
This spell closes all wounds, neutralizes any poison, heals all diseases and raises curses that affect the creature when it died. The spell replaces damaged or missing organs and limbs. If the creature was not dead, it is restored to its living undead form.
The spell You can even provide a new body if the original no longer exists, in which case you must pronounce the name of the creature. The creature then appears in an unoccupied space that you choose 10 feet from you.
By my aforementioned interpretation of WoG, this spell will qualify for the exemption only If it is not used to create a new body. If the spell is used to create a new body, we are now in Clone territory, and therefore we no longer qualify for the cost exemption.
In summary, we can comfortably say that Raise Dead, Revivify, and Resurrection are qualified for the cost exemption offered by WoG. True resurrection may or could not Rate, depending on how the spell is used.