For the most part, chess has been called the game of kings since the king piece in chess is the center of all objectives involved in the game. It essentially means a game with kings that fight each other. This naming system is similar to what a lot of beginners do when they describe a game that they ever see, which is the objectives of the game and how it is visually played. Chess was originally called the Game of Kings in a past era in India (where the game originated) because the central figure is the Shah or King. The game ends in Shahmat (literally, The King is Dead). Shahmat is actually the word where checkmate is derived from, a lot of things in chess focuses on the king, protecting it, and attacking it that people will start noticing.

Source: WGC