Eh . . . I don't think the downvote was out of pure malice.
An Analysis of the Post
A quick summary
I read through the comment thread on that question, which was between you and the other user. Comments 1-8 seemed perfectly normal, discussing some confusion that had come up. The user ended comment 9 by saying
Let me add that I have no incentive to force you to see the light if your main concern is to stonewall the approach (2.) against criticisms, although (2.) is at present squarely wrong.
If I'm reading this correctly, s/he felt that you were not accepting criticism properly.
You then wrote four comments in a row about different aspects (written too far apart to be put as edits into each other). The last one was posted today (the previous three having been written in November), to which the user responded
Well, if you are happy with yourself this is already something.
I think you interpreted this as sarcasm. Perhaps it was, perhaps it wasn't. I don't know what the user meant by it. Your response was
I was happy with myself when I've found out where the actual problem was some months ago, I've posted it here to help the others who had the same problem and I was also hoping you would appreciate the feedback. I was obviously wrong about the latter. I was as unhappy with the answer you've provided then as I am now with you down-voting my correct one without any constructive feedback. For me, that is a poor reflection of your attitude and I truly hope you are not as malicious as this makes you seem to be
The user's response to that was
The thing is that I have had to battle like crazy to help you and that you steadfastly refused to listen. But you are right, all the fault is on me. Happy? (And to see that you invoke "constructive feedback"... well, I guess chutzpah does not kill, does it?)
You then followed up with two more comments. Neither seems to be particularly inflammatory, though a tad accusatory. There has been no response since.
What it all means
This is a case where both users feel that the other is being overly stubborn and is not behaving cordially. This happens sometimes, though generally not a lot to a given user, unless s/he is a moderator, and happens to be unlucky enough to have to tolerate a lot of crap from folks who really aren't interested in contributing anything positive.
In short, both of you have come away from the whole thing - at least at what may be a ceasefire - thinking that the other is being unhelpful. This is, to be frank, the worst thing that could happen. Fortunately, you brought it up on meta.
I honestly don't think that either of you is justified in calling the other "malicious". I can see that you think that of him/her, and I would wager that s/he thinks the same as you. Neither of you can really pretend to be innocent - I'll be frank. Both made some semi-inflammatory remarks over the course of the conversation. Perhaps the blame doesn't rest on the shoulders of just one user. In that case, the course of action changes.
What to do
Whenever something like this happens, a neutral third party is needed. Yes, I'm talking about one or more moderators. Solving issues like this is one of their jobs - not a common one, and not one they relish (I certainly don't), but a job nonetheless. The moderators on this site are good at their job. I've been fortunate to interact with some of them on cross-site things, and they're well-suited to their job.
I suggest that the first course of action for you is to talk to a mod. Don't flag anything; go straight to them. They have an office in chat. I haven't been there, and I can't speak for them, but I think that they'll be happy to help, in some way, shape or form.
After that . . . well, that's their decision, not mine. Speaking as a mod from somewhere else in the network, I can say that I would get another mod and both users and create a private chat room, and then metaphorically sit everyone down and figure this thing out. I would bet that the mods here would do something similar, but I wont put words in their mouths.
Mods can and may do other things. They could contact users via email - though this is only typically used for major offenses, such as suspensions - and they can delete comments, which I suspect will happen at some point (though the comments may instead be imported to the chat room, for reference).
If you don't want to do this through the mods - in other words, if you feel that the dispute is serious - then you can just create a private chat room for you and the user - I believe you have enough rep for that, or at least one where only the two of you are allowed to "talk" - and sit down together and talk it out. There are cases where one of two parties may not be willing to do that. Then perhaps it would be wise to call in a mod. But if you think you can talk it out one-on-one, then all the better. You've saved someone's time, and almost certainly yours.
On the downvote . . .
I can see that the user disagreed with one of your steps early on. I can see no point at which s/he ever relented. I still don't know which of the two of you is right; this stuff is over my head. But if s/he disagrees with the solution, then the downvote wouldn't be out of malice. It would be because the user thinks that the answer is incorrect. That's okay. The user could be wrong in thinking that, but they are allowed to downvote, if they believe that a post is downvote-worthy.
I could be wrong now. But I don't think so. Well, perhaps I am. I really can't say. In any case, I'd be willing to give the user the benefit of the doubt, rather than jumping to conclusions.
'Course, there is a way to find out. . .