What exactly is perfect play? Can there can be multiple perfect plays, which sounds quite contradictory? If perfect play is known for all openings then why would a player play anything other than that? Such a thing would make all high level games futile because then players would intentionally divert from perfect play in order to just create a show or something similar.
In the context of game theory, perfect play involves playing truly optimal moves. Specifically, if the game state is a (theoretical) win for the player to move, perfect play would be a move that both preserves that state (eg keeps the game a winning state) and minimizes the number of moves remaining until victory. If the game state is a draw, perfect play preserves the draw. If the game state is a loss, perfect play cannot improve the theoretical outcome, but instead maximizes the number of moves until defeat.
Perfect play is, by definition, known for solved games like Tic-Tac-Toe. Chess is not yet solved, so in most board positions, perfect play is not known. For some situations, for example positions with 7 or fewer total pieces on the board, we have endgame tablebases which have perfect play recorded. Also, for positions with forced checkmate in sufficiently few moves, engines can calculate perfect play on-the-fly by simply looking at all possible moves and responses and choosing one that gives checkmate the fastest. Perfect play is not (yet) known for chess openings. If chess were solved and perfect play were widely known, then it is possible competitive chess may die.
There can be multiple perfect moves for a given board position. For example, if there are two different moves that immediately checkmate the opponent, both are perfect. Playing around with endgame tablebases, it is fairly common to find positions where multiple moves lead to checkmate in (say) 18 moves. If the game is a theoretical draw, often many moves preserve the draw. All of these moves are perfect from a game-theory perspective, though some may give better practical chances than others.
Technically, perfect play would consist of making moves that do not adversely affect the result of the game. In endgame theory books, only mistakes can change the result, and they are flagged as such. Strictly, in a winning position, you might require that perfect play reaches the win the the smallest number of moves, or conversely postpones the defeat for as long as possible in a losing position.
On either of those definitions, there may be several equally good moves in a position. A chess engine announcing a mate in 5 (or 15!) may see multiple different routes of the same length to checkmate.
That's the game theory answer - John Nunn takes that approach in his endgame books, for example.
However, there are the twin facts that chess is not yet solved (so we do not know the perfect play) and you may be facing a human opponent who is both fallible and has particular strengths and preferences. I would argue that best play in this case would choose the moves that are most likely to lead to a win today against this particular opponent - which might not be (game-theoretic) perfect play. Playing moves which are not theoretically best in order to maximise winning chances in a real game introduces an element of risk.
Finally, sometimes in a tournament or a match, a draw is as good as a win. In those circumstances, the change in the relative value of the outcomes would lead to a different optimising solution for the practical approach even though the game-theoretic solution (if it were known) would be unchanged.
1. What exactly is perfect play?
Firstly, the definition of perfect play is very subjective. One may say that a 4-move checkmate is a perfect play for me! Or, the best possible move that you could have done regardless of the situation you are in, "Oh! that was a perfect play because you could not have played any other move any better!".
According to me, a perfect play is when the entire game is always in your control. In the sense that, with every move you make, you force your opponent to make a move of your choice rather than his own choice. This is not possible in the game of chess. You can predict the probability of a move, but cannot force an opponent to play moves in every given scenario unless you are some intelligent silicon-based life form that can simulate every possible scenario. Therefore, according to my definition of "perfect play", it simply cannot exist.
2. Can there be multiple perfect plays?
Maybe according to some other definition of a perfect play.
3. If perfect play is known for all openings then why would a player play anything other than that? Such a thing would make all high level games futile because then players would intentionally divert from perfect play in order to just create a show or something similar.
Well, if perfect play did exist, then no one would willingly play anything other play than that, unless given good enough motivation (e.g. bribery) during competitions. That is the only logical answer here.
I am not sure whether there is a single definition of "perfect play".
The answers so far considered perfect play separately for the winning or losing player. In this sense it is often used in the negative sens: white's position is lost, even with perfect play
However, "perfect play" can also refer to the combined play of both players. As such it is what you get if the winning player is minimizing DTM (depth to mate) while the losing player is maximizing DTM. So basically what a minimax engine does.