I find this somewhat of a non-issue.
"He Retains the Advantage" - The Importance of Pronouns in Chess

it has developed into society that he represents mankind, and thus the pronoun "he" is appropriate for usage. Although it would possibly be better to say he/she, using he is fine.

Actually, I kind of like those parentheses I used -- he (she), his (her). I like it a lot more than "his or her" for some reason. But probably most people would hate the parentheses -- I have a soft spot for parentheses though. Anyway in this case the parentheses would imply that you could skip them and the passage would still make sense, but, if you want confirmation that the author isn't sexist, bam, there you go.
Just one problem -- do we say she (he), or he (she)?

It's worth noting a distinction: in some cases it's natural for me to use "they" and in other cases "he" (although "she" works just as well). I feel like "she" (or "he") sounds natural in some kind of influential quote like "a person ought to do this, take care of her kids, respect herself, bla bla bla," but "they" sounds more natural in a sentence like "whoever wins, they will receive this."
Again I think "he" (and sometimes "she") is more likely to be used if you're speaking of this faceless example person that represents both genders. "They" seems natural in some singular situations, but not in that one.
But Alison, I want to point out that I do agree with your general sentiment that the appropriate terms to use are not necessarily determined by a grammar book but by whatever communicates the best. If you have to break a grammatical rule to make a point, well, in that case, you'll actually communicate better that way!

"the claim is that it's 'tradition' to use 'he' (the same claim that kept women from voting *ahem*)"
Uh... does "he" keep women from voting? Everything would mean exactly the same thing regardless of what word we used to symbolize it. We could start using the word "banana" to mean "a boy," and it wouldn't make them any less a boy in the way we understand them.
If we could just change tradition right now, sure, why not. But the practical issues with it shouldn't be underestimated. What if we wanted everyone to say "apple" in a different way? You know how hard that would be? Thankfully, though we wouldn't be able to change the use of "apple," we don't have to because we know what it means. The same applies for "he."
Any protests and such spent on pronouns would be really wasteful because even if they succeeded, the meanings of books would be exactly the same, and imo it would solve almost nothing. Meanwhile, all that time could have been spent on a true women's issue, that actually affects their lives.

One more point is that probably almost all of the words we use have strange origins. Even the words in these two sentences. Who knows why tradition passed on to me to use the kinds of words I'm using right now in this paragraph. I use them because they're simply ingrained in me. I wonder why certain accents emerged the way they did -- whatever the reason, it has nothing to do with why I have the accent that I do -- I use it because it's my only way of speaking, and dammit it works. I never would ask my parents why they are telling me to say words a certain way; I just said them.
Women have many reasons to complain. Being raped and hanged in India; abducted from school in Nigeria and sold into marriage; suffering the pains of childbirth and the discomforts of the menopause the world over.
Pronouns, however, don't begin to hack it.

"In go, when writing about a game between two abstract opponents, one is generally referred to as "he" and one as "she"."
Haha, that's awesome. Very cute.

But seriously, is it not easier and quicker to default to "he" rather than "he or she" and all the rest?
I have an answer, even though it really isn't feasible since it would require concerned members of chess.com to lead a movement to replace "he" or "she" with the even simpler "e". If enough English speakers started using it, eventually it might catch on.
In context it should be easy to understand ("e moved the king to..."). You could all start doing it and within a few years maybe others would pick it up. Who knows? We would have lead a new movement. Of course, at first everyone would think we were just lousy typists, but that is true anyhow, so who cares?
It sure beats "they".
I haven't thought about what to do with "his" and "her" but my brain is only big enough to solve one puzzle at a time.
One more point is that probably almost all of the words we use have strange origins.
Some origins are not so strange. Using 'he' to refer to men and women originated from "intellectuals" who forced it on society in the 19th century. Before this, writers such as Shakespeare happily used 'they' when referring to a single person.
On the other hand, 'man' did used to mean a person, either male of female, as per the Germanic origin of English. This legacy remains in the words 'mankind' and 'manslaughter'. Around the time of Chaucer, 'man' began to take on the modern gender specific meaning.
As an aside, the word 'wer' was used to mean a single male. Hence the origin of the word werewolf.

r_k_ting -- you're missing the point. In my post I went on to say why the origin doesn't really matter.
Of course it doesn't matter. What matters is ensuring that no one feels excluded as part of our chess community, or the wider community. That's why book publishers have progressively eliminated the use of 'he' to mean women.

The problem with using something other than "he" such as "they" is that implies more than one person.
People don't want to be misunderstood so....I mean its reasonable to use the masculine term "he"

Of course it doesn't matter. What matters is ensuring that no one feels excluded as part of our chess community, or the wider community. That's why book publishers have progressively eliminated the use of 'he' to mean women.
I'm saying that she shouldn't feel excluded based on that. You might think wow, look at this horrible guy telling her how to feel. Well, the meaning of the pronoun has been made clear; in my honest opinion, anyone who insists that it still means "only men" is not even trying to understand what they mean.
If one insists that there is only one meaning of "he," well what can I do, a person can insist whatever they want. But if they just insist something arbitrarily I'm not going to feel responsible for them. Sometimes, and in this case, life is so much easier if you don't create problems when they aren't there. It takes a lot less effort to realize that than starting an entirely new tradition, so that, somehow, everyone in the world follows it. That kind of effort makes more sense to place in true women's issues, of which there are plenty.

An example I would give as a "real" problem is if authors really did think that only men could play chess. And perhaps there are some sexist people like that. However, you cannot tell simply based on what pronouns they use; that would be far, far too presumptuous.

Mind you, if I became a chess writer, I probably would end up using "she" just because, as evidenced here, people misinterpret things. It just seems like a more practical choice. But I don't blame writers who use "he," because it's perfectly legitimate.

God is a “He”.
We are made in “His” image.
But God is genderless and has no physical form.
Go back to the HMS Sheffield post and replace the word ‘She’ with the word ‘It’ and see how the information presented has become somewhat deadened, that something has been taken away rather than added.
This is because we are feeling beings, not intellectual beings. We know what is right whilst the mind only thinks it knows what is right.
"It would 'annoy' male players if suddenly the feminine pronoun slipped into general usage......"
I know you're happy Alison, but you've got one problem left: I'm a male chess player and wouldn't be annoyed by it :)
Good luck trying to get me annoyed by it :)