[RPG] Is a Gorgon’s Petrifying Breath a poison attack

The Green Dragon's breath is described as:

Poison Breath (Recharge 5-6). The dragon exhales poisonous gas in a 90-foot cone. Each creature in that area must make a DC 22 Constitution saving throw, taking 77 (22d6) poison damage on a failed save, or half as much damage on a successful one.

It is "poisonous gas" the Dwarf gets advantage on the save.

Poison. Venomous stings and the toxic gas of a green dragon’s breath deal poison damage.

It is "poison damage" the Dwarf takes half damage (effectively 1/4 if saved 1/2 if not).

With respect to your comments on protection from poison, I think you are splitting hairs: it is poison so advantage is given on the save; the fact that the effect is to do poison damage rather than impose the poisoned condition is irrelevant to the save.

That said, the DM is the sole authority on rulings so, check with your DM.

Let's consider a different question for a moment. Suppose I'm building a monster, and I give it a melee greatsword attack with +4 to hit and 2d6+4 damage. How much CR does that add?

Well, it depends. If my monster was a huge dragon and it already had a bite attack that's way better than the greatsword, then the greatsword never gets used and it adds no CR at all.

On the other hand, if my monster was a ratling and its previous best attack was a dagger for 1d4+1, then the greatsword is actually a big deal.

So the answer I'd propose is: if you add an attack which the monster is going to use as its primary attack, you don't "add" to the Offensive Challenge for that. What you do is you figure out the Offensive Challenge for that attack, and you have just set the monster's Offensive Challenge to that number.

So: what is the Offensive Challenge of a petrification attack? What other monsters can we find that have petrification attacks, and what is their Offensive Challenge?

The basilisk has a similar power, except it's attached to a Constitution saving throw, DC 12. This power is the basilisk's most dangerous attack, so the Offensive Challenge of the attack should be about the same as the CR of the basilisk. The basilisk is CR 3, which, uh, seems kind of low actually for a save-or-die attack. The CR for your power might be lower still, since it requires an action to use and only affects one target at a time.

The medusa also has this power, except in the medusa's case the power is DC 14 and the CR is 6. Maybe we could make sense of this by saying that adding +2 to the DC means +2 to the CR, and the medusa also has a snake hair attack which is pretty dangerous, so maybe that increases the CR by 1 since the medusa can do both at once.

So I think the answer to your question will depend on the DC of the ability.

If I could add a note, as well: in my experience, fighting monsters with save-or-die attacks is frequently not fun. Either the player character makes the save and the monster's attack does nothing, or the player character fails the save and now that player is out of the game. You might consider replacing the save-or-die with something that does (for example) ability damage.