You may have met a troll (intentional or not). Don't worry, the Stack's got you covered.
This is actually really easy: you do nothing. Nothing different to normal, that is. All the habits you've developed interacting with good-faith users are going to fix this problem, too.
If someone's truly acting in bad faith, keeping to your usual behaviour will make them stick out like a sore thumb; if they are in fact trying to act in good faith but are making mistakes then that can get resolved sooner or later with a positive helpful experience along the way.
Stay Calm
You leave a comment in good faith, OP seems to misunderstand or disagree, you respond again, another response from OP, and you're starting to get annoyed.
Step away. Calm down. It's not your job to convince someone else they're wrong or make them see your way. Your first comment, presumably, did a pretty good job of summarizing what you saw as problematic. Just leaving that one was a courtesy, an attempt to help another improve their post. If your first comment isn't well-received there's no burden on you to make it get a good reception. (And you can't, anyway.)
In other words: act exactly the same way you would in any other case.
One or more of the OP's comments or chat messages strike you as getting hostile, aggressive, rude, &c.
Flag it as "rude." Just as you would if I left a message you find hostile or rude.
But it's not rude. There's nothing overtly hostile. In fact, OP is "signing off" a lot of comments with "Thanks!" and "I appreciate the considered response!"
Remembering that comments are intended to improve posts, if it seems comments are descending into a conversation about something other than the post, flag as "not constructive." It's not a conversation button, it's a comment button. And "comment" has a very precise meaning around here. (See also these meta posts (1, 2, 3), along with just about every meta about comments.)
In other words: act exactly the same way you would in any other case.
If in doubt, if things seem to be going off the rails, raise a flag for moderator attention and explain what you're seeing as a problem.
Remember, we try our best to keep this site unrelentingly focused on productive behaviour to keep it safe from trolls. When we work hard at just doing what we usually do, someone isn't making effort to be productive will stick out like a sore thumb: trolls out themselves.
Pop into chat (for those with 20+ rep)
You're getting a strange feeling, but feel like flagging is really extreme. You don't want to get someone in ~trouble~, after all.
If another user's comments and/or activity strike you as odd go ahead and pop into RPGSE's main chat room. There's usually a good amount of experience lurking around there, so "hey room, can I get a sanity-check here?" will usually get a response. More eyes, more (aggregate) experience, perhaps a few more votes and comments... all of which are the mechanisms by which the site is designed to operate.
On occasion OP will also be in chat, and you can see they're starting to workshop the question with others. Join in. Or don't. Whichever you prefer!
In other words: act exactly the same way you would in any other case.
Quietly disengage
You've interacted--voting, commenting, perhaps a meta post.
Recognize that at this point you've gone well beyond anything that is required of you. Remember: no actions are required of you to use this resource. Anything you do is a volunteer effort.
If you are not enjoying the interaction or do not think it is helping, just walk away.
That was easy. Thanks, Stack.
P.S.: this is exactly the sort of community moderation that has led to feedback about us being "the most heartwarming place in whole SE" (source) or someone expressing it's "a bit flabbergasting to find the Roleplaying Stack Exchange is a healthy community full of knowledgeable, considerate people." (source)
