Many players already have played a perfect game where no mistakes were made. These are often short games where a draw is agreed to early.
1. e4 e5 2. Nf3 Nf6 agreed drawn
Actually there have already been thousands of perfect games played.
If the game is short you do not need a super computer to tell if the game is a perfect game.
How do you know that it was not a mistake to offer/accept the draw? Nobody knows the result of best play from that situation. The game may have no mistakes, but we do not know that. It is possible (although unlikely) that all six playing decisions were mistakes in that game.
Actually it is you who brought up things such as considering what the players think makes some difference in a perfect game. It is what the players actually play which makes a difference.
I did not say anything about considering weanesses in players you did when you said agreeing to a draw when there are some winning chances is a blunder.
"perfect games" have nothing to do with what the players think or if they have winning chances. "perfect games" are games without errors.
Even a player who has been playing one week can sometimes play a perfect game.
You seem confused as to what is a perfect game.