This looks significantly better in terms of covering all possible situations, save for the following:
Clarifying the rules on the Pawn's double step that Reiniger mentioned
Does the double step for Pawns also apply to White Swans?
A distinctive piece image for the Black Swan
The movement of the Black Swan
There are other improvements that could be made as well, but these shouldn't really be a blocker to publication.
If a White Swan coming from the first rank gets flipped over on the second rank, it can be subject to capturing.
This should be in the Rules section in my opinion, if it is meant as a rule. You may want to be careful with this though, as you may encounter a problem with having to keep track of which White Swan started where, and thus which ones are able to be captured.
This looks significantly better in terms of covering all possible situations, save for the following:
There are other improvements that could be made as well, but these shouldn't really be a blocker to publication.
This should be in the Rules section in my opinion, if it is meant as a rule. You may want to be careful with this though, as you may encounter a problem with having to keep track of which White Swan started where, and thus which ones are able to be captured.