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Can I comment here by saying that what is on the AbstractGamers wiki page
is a first attempt at this?  It needs a bunch of work.  Some issues are
easy to deal with.  In the case of Othello, since conversion is mandatory,
all you need to do is record where the move took place.  Cases where
capture is mandatory, it isn't a problem.  The issue becomes when you do
an action, and it is not mandatory.  That is an issue that needs to be
resolved.  I am not sure what solution people use today in games where if
you do a capture vs a non-capture move.  Say, you have a case of checkers
where you can jump, but you may or may no decide to choose to take a
piece.

Anyhow, more work needs to be done here on this.  I would expect others to
come up with solutions.  The idea here is to have something that works.  We
will both need to have a FEN solution for storing position, and a common
standard for communicating moves.

In regards to a 'FEN for movement', FEN was used to describe a method
for recording game states.  The 'FEN for movement' comment, even if it
was a poor phrasing, was meant to state a format that would describe
moves, the way FEN is used to describe game states.