A couple of things I noticed when I glanced over the website-
"In order to get yourself into a position where you can trap your
opponents King, you will need to try and capture as many of
your opponents pieces as possible."
No. No. No. The Opponents King can be surrounded by his pieces and still be checkmated! Don't give misleading advice!
"Whenever you move one of your pieces into a "Checking" position,
you MUST let your opponent know by verbally saying "Check". "
MUST? No. It might even be considered rude to say Check.
"If your opponent is put in "Check", he/she is obligated to move their King into a position in which they are no longer threatened. This can also include moving another piece in between the King and the attacker in order to protect the King.
If your opponent cannot find a space to move their King where it will not be in danger of capture on the next move, you have put them in "Checkmate"."
That whole section seems to need work to be clearer. Plus, A King or his army may be able to CAPTURE an attacking piece to get out of check.
Concerning castling-
"The King cannot be in check when the move is initiated, nor can he end up in check after the move is completed."
And the King cannot move THROUGH check either.
I'm not trying to be "mean", I hope this helps you improve your website. And maybe it wouldn't hurt when describing how the Chess board is set-up to mention about the White square is always in the lower right hand corner. You show a diagram and where the pieces are placed but it wouldn't hurt to spell it out for the beginners.