In early Sanskrit chess (c. 500–700) the king could be captured and this ended the game. The Persians (c. 700–800) introduced the idea of warning that the king was under attack (announcing check in modern terminology).
This was done to avoid the early and accidental end of a game. Later the Persians added the additional rule that a king could not be moved into check or left in check. As a result, the king could not be captured, and checkmate was the only decisive way of ending a game.
Before about 1600, the game could also be won by capturing all of the opponent’s pieces, leaving just a bare king. This style of play is now called annihilation or robado.
In Medieval times players began to consider it nobler to win by checkmate, so annihilation became a half-win for a while, until it was abandoned.
In modern parlance, the term checkmate is a metaphor for an irrefutable and strategic victory. The term checkmate is, according to the Barnhart Etymological Dictionary, an alteration of the Farsi phrase “shāh māt” which means, literally, “the King is helpless”.
Others maintain that it means “the King is dead”, as chess reached Europe via the Islamic world, and Arabic māta means “died” or “is dead”. However, in the Pashto language (an Afghan language), the word māt still exists, meaning “destroyed, broken”.
Moghadam traced the etymology of the word mate. It comes from a Persian verb mandan, meaning “to remain”, which is cognate with the Latin word maneō and the Greek menō (μενω, which means “I remain”). It means “remained” in the sense of “abandoned” and the formal translation is “surprised”, in the military sense of “ambushed”. “Shāh” (شاه) is the Persian word for the monarch.
Players would announce “Shāh” when the king was in check. “Māt” (مات) is a Persian adjective for “at a loss”, “helpless”, or “defeated”. So the king is in mate when he is ambushed, at a loss, helpless, defeated, or abandoned to his fate.
In modern Persian, the word mate depicts a person who is frozen, open-mouthed, staring, confused and unresponsive. The words stupefied or stunned bear close correlation. So a possible alternative would be to interpret mate as unable to respond. A king is mate (shah-mate) then means, a king is unable to respond which would correspond to there being no response that a player’s king can make to their opponent’s final move.
This interpretation is much closer to the original intent of the game being not to kill a king but to leave him with no viable response other than surrender which, better matches the origin story detailed in the Shahnameh.