well maybe chatting while playing is distracting to her and she would rather focus on the game?
Terminating a Game

Maybe. And I have no problem with that. The solution is then to just not chat. I had no intention of getting into a long conversation anyway. But the measure she took to prevent chat is not quite the same as simply not chatting.

you dont go to the gym to avoid talking to people to focus on your work out routine. she disables chat to avoid talking to people to possibly focus on her strategy finding tactics and looking at variations during that game. without her input we really have no idea why she takes this but to assume she is weird we can also assume she is doing it for similiar reasons as you not going to the gym.

But there is still a distinction here. I do not go to the gym. She could choose not to join Chess.com (and certainly not to join World Friends). Or she could join Chess.com and not accept my challenge. But imagine if you and I agree to go to the gym together as work out partners, so each one can motivate the other to train harder, and maybe also for proprioceptive stretching (a form of stretching that generally requires a partner). Now we get there, and at this point I put on my ear phones to block you out.

ahhh but here in lies the problem to "workout" at chess doesn't require one to talk to thier opponent however when working out in your situation it requires communication to be effective. and your orginal example was on a treadmill single activity also not requiring communication. The point and difference is you both agreed to do a mutual activity that requires some form of communication a chess game does not require communication so for a person to choose not to communicate in your example would be weird in a chess game it is optional therefor shouldn't be considered weird or not normal.

For full disclosure, I described the experience as weird. I do not believe that I used this word, or any other insulting word, on the other player involved. It still strikes me as odd, but perhaps less so now than it did before, so I thank you.

Yes, I did say that, and I meant it as an appeal for someone to explain human nature to me (which MCASH and a few others have now done). That is not quite the same as calling her psychotic, is it?

You are correct at least for the first 3 pages as im not going back to re-read everything, however based on comments and things said it has been implied, the fact that her disabling the chat is weird implies she is weird.
no it is not but throughout your posts and discussion about this either indirectly or directly you and maybe others have pointed out the unnormalness aka weirdness of this person for not wanting to chat during a game. weird i can kinda understand but to label it as hostile i honestly don't think ill ever be able to understand how you or anybody could come to that conclussion but you are more then welcome to try.

I found it hostile, and I am the only one qualified to discuss my own interpretations. I make no representations as to what she was thinking when she did it.

well then i could say based on your actions and descriptions i could interprete you as a stalker or some kinda freak overly obsessed with playing only women who will chat with you, however i won't cause it is probably completely off base and farthest from the truth. i can also find your obsession with chat in general and your over reactions to those that don't chat hostile. but again i don't because there isn't enough to base any assumption on and i have more substance to base those on then you do of why this person doesn't want to chat.

Okay, so I concede the analogy needs tweaking based on Vance's input.
Vance's perspective is that her exercising using the treadmill is more analogous to Tactics Trainer here.
And Vance would say that (continuing using the exercise metaphor), it is more like she went to the local basketball court where there are typically pickup games - more specifically 1-on-1 games. And yet after talking just enough to agree on the game type and time, she still engaged in the same behavior described above as on the treadmill (earplugs, averting gaze, etc.).
So yes, that may be seen as anti-social, but not as hostile, IMHO. Now if she's "shutting out" her opponent in a "shared game" - that may be called cold, but it's not like she's trash-talking or aggressively invading your space (online chat equivalents would be typing offensive remarks and/or asking personal questions).
By disabling chat, she never gave Vance a chance to show that he can play straight-up chess without the chatter. But she also never gave him a chance to bug her either.
My guess is that if she had all those other channels cut-off (no messaging or notes), she has had a bad experience in the past and is either continuing to protect herself from an individual and/or trying to avoid a repeat incident.
Now Vance further states that this seems contrary to being in a group called World Friends. But she could have been a member of the group way before she had to adopt this reclusive-esque behavior. And if she belonged to that group before and later suffered an incident such as this, I certainly don't think she would (or should) quit because the name implies instant-conversation; she has trust issues, clear and simple and they may have valid roots.
On the court, why should she stop frequenting a favorite spot just because some jack-hole harrassed her once or many times? But then, why should she act like she assumes every stranger is a jackhole?
Vance, in the end analysis, there was err on both sides - the likelihood was that you both made assumptions. But given time and respecting her silence was probably based on a (good) reason, then you may have earned her trust after playing a honest game or two and re-challenging her.
If after about 5 games, not a pip? Then she's obviously not the friending type anyway, but you would possibly could have begun to erode her doubts about men on the other side of unsolicited challenges.

Maybe she wants to play to chess and not talk to idiots? Maybe if she wanted to chat to some one she can do this with actual people? Maybe she doesnt care about your inflated sense of importance?

proprioceptive stretching (a form of stretching that generally requires a partner)
I want to come clean, and own up to my mistake before somebody else catches it, and blasts me for it. Proprioception refers not to stretching but rather to balance, and is said to help prevent sports injuries. The partner-assisted stretching I was trying to describe is actually PNF stretching, if memory serves correctly.
I see your point, but I am not so sure that the analogy works. As one who works out myself, on the treadmill and off, I know how distracting chat can be when working out. In fact, this is why I almost never go to a gym anymore, and instead just work out at home, or at the track. It might be the same way in blitz chess, but we are talking here about turn-based chess, so I cannot really see how chat is distracting. Nor, for that matter, did I ever say that I was holding out for chat anyway.