Okay, guys.
Here are the short rules of Gravitatur Chess:

Only King can make a capture.
King can swap with its friendly piece but not Pawn.
Chess pieces can threaten the opponent's King.
No castling, no en passant.
Gravitatur attracts all pieces towards itself and then removed from the board.
If a player is in check, there is no use of Gravitatur.
At the end of the player's turn his King is not allowed to be in check.
All the rest rules follow the rules of Standard Chess.

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More detailed here:

boardgamegeek.com/thread/3417720/gravitatur-no-capture-chess

and here:

www.chess.com/blog/Pokshtya/gravitatur-chess

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