Oh come on now, if you didn't think this foreshadowed some of the deaths, many of which did come to pass, including in the immediacy when she ordered Jaquen to kill several nearby names on her list, then you're just refusing to see it is setting up for the reader a thirst for vengeance. Arya will get Joffrey. Or Robb. Some Stark will.
Instead he is killed by a conspiracy we don't understand for hundreds of pages (or a number of episodes) that doesn't involve the Starks, and it ends up getting another character we like (Tyrion) sentenced wrongfully to death.
No, I think that being foreshadowing would be terrible writing. It's not a subtle hint what's to come, it's outright saying, over and over again, that Arya will try to murder them if she gets the chance. It's just establishing character and externalizing her hatred. Martin isn't a terrible writer without subtlety.
The result is even more in my favor. It clearly wasn't a foreshadowing, it was just her character speaking her desire. It's not something I would see as a red herring, which it would be if it was actual foreshadowing being a misdirect.
You mean like "Red eyes, blue eyes, green eyes?"
Yes, that is something that actually can be seen as foreshadowing (although it's brown eyes, not red eyes), as it's something vague from a source that actually can see something of the future.
However, what she says is that she sees darkness inside Arya, and within that darkness eyes that stare back. Brown eyes, blue eyes, green eyes. Eyes sealed shut forever. The likely foreshadowing isn't that Arya will kill people but that she will have those eyes. Meaning that she will follow the god of death and become a faceless woman with the eyes (and faces) of dead people.
It's pretty telling that they changed the quote when they brought it up again. Melisandre would probably have been a lot more interested in Arya if she saw a connection to the Night King.
I honestly never put much stock in the Azor Ahai prophecy. It is too vague and the person who was the must gung ho about sharing it got it wildly wrong by betting on Stannis, who clearly was never it. Words are wind is a common refrain in the show. Only Maggy the Frog's prophecies have had much validity.
So you're saying that you don't put much stock in the prophecy that gave the story its name because it's vague and Melisandre has interpreted it wrong? That's pretty funny as you brought up her comment about the eyes, which is far less substantial to the subject of the Night King, not even consistent between the two times it's been mentioned, and from the same source.
Unlike the eyes comment the Azor Ahai prophecy is shown to the readers from many different sources and it's a pretty central thing in the story, unlike the eyes one which isn't even in the books at all. While Melisandre interpreted the identity of the Prince That Was Promised wrong we still get to see R'hllor show her the truth. I don't think it's wise to dismiss a prophecy just because a character doesn't interpret it right (that's standard with prophecies) when the actual god, that has directly intervened through his priests, is weighing in on it. That prophecy is very much in play.