Revenge Chess is the intriguing cross between Chess and the basketball varient Revenge. For those who don't know, the main idea behind Revenge is that you remember who got you out, and when that person gets out, you get to come back in to the game.
What this means for Chess is that when a piece is captured, it remembers what it was captured by, and can respawn when its captor is captured. The respawning piece will respawn into the square it started the game in. If there is another piece occupying the square which the respawner is supposed to go, the respawner captures the piece in the way, regardless of the two pieces colors.
Other than the respawning (and minor changes that I'll go over in the next paragraph), the rules are identical to those of Chess. I won't go over what those rules are, because there are much better tutorials online than what I can produce.
There are a few minor rules to keep in mind. This game supports En Passant (if you don't know what this is, I've found the Google Image results for "En Passant" to be the best explanation). However, it does not support pawn promotion (getting a piece back when you get a pawn to the end of the board), nor does it support castling (that weird thing the king and rook can do). In addition, there is not Check nor Checkmate, instead, the king has to be captured. The reason for this is that there exist interesting strategies that involve sacrificing your king, and having the resulting cascade bring him back to life. So, instead of the game ending at Checkmate, the game ends when a player's turn ends without one or both of the kings being on the board.
Lastly, I'll go over the controls and user interface. The bar in the top-right displays who's turn it is to play, as well as displaying the winner when the game ends and holding the "reset" button. When you hover over a piece, its name will be displayed in the tan area, and below its name will be the names of each of the pieces it has captured. Also while hovering, a red dot will be displayed on every square where something will respawn if the piece is captured. When you click on one of your pieces on your turn, a purple dot will be placed on every square that it can move to. Click on a square with a purple dot to move the selected piece that that location, or click on an invalid square to deselect the piece.