What is the process for amending the rules of chess? I read the whole document issued by FIDE containing the Laws of Chess, but nowhere does it say how (or even if) the rules of chess can be amended.
Is every change to the rules supposed to yield a new variant? But then, what about minuscule changes like allowing the king to castle out of check, or slight tweaks on how en passant works? If, for example, the double-advance rule for pawns had never been invented, would there really be no way of introducing it into chess now? Would we just end up with &quot;standard&quot; chess and &quot;pawns-can-move-two-squares-forward-on-their-first-move&quot; chess?
Plus, a way of changing the wording of the rules must exist—when the rules where amended to explicitly disallow vertical castling with a pawn that had just been promoted to a rook (which the rules accidentally allowed previously), someone did manually rewrite a portion of the rules in a way that was binding for everyone else.
So what is this way, and who can do so? Is it FIDE? Are there any meetings that take place according to a regular schedule where potential changes can be submitted and discussed? Who can submit these proposals, and once they are approved, are they binding for all national federations?
FIDE has a Rules Commission (https://rcc.fide.com) which reviews the Laws of Chess every four years according to their FAQ. I don't know about the process itself, but if I had to guess I'd say it involves lots of committee meetings and emails. :-) One interesting detail, though, is that they have a form you can fill out with suggested changes to the Laws: https://rcc.fide.com/form-of-loc-change-proposal/
But like the FAQ also says,

Considerable changes were made in the 15th century. The scope of the queen and bishop in particular were increased then. This made it a much faster game. The Laws are reviewed every four years, but these are either just tidying up, or changes to the Tournament Rules.

So don't expect any changes to things like how the pieces move, other than possibly closing of loopholes like the one about vertical castling which you mentioned (are there any loopholes left? That's a separate question).