Is there such a thing as a unique chess playing signature? Is there such thing as a chess playing signature? Meaning within x-amount of games the identity of a player is known based on the skill and game play of the player.
Unlikely.  The first several moves of any game by notable players are all book.  Thereafter, people who play notable games are able to play superb offensive and defensive moves.

Now, if you see some crazy sacrifice, you might think Anderssen or Tal is playing this game. Similarly, if you see some superb positional move, you might think Petrosian or Karpov is playing.

But to see a game played by any of the top 20 players of all time and pick out who was moving the pieces based upon their styles, I can't imagine it.  There simply isn't the 'bandwidth' for such an individual signature in chess beyond someone playing more positionally or more tactically; that's pretty broad-brush stuff.