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That honour probably goes to the Ancient Egyptian game, Mehen which dates back to pre-dynastic times. The rules of the game are not known, but surviving examples have been found with up to six playing pieces, and it is believed that these were counters for up to 6 players.
An instance of the game being played by a group of four players is portrayed in a scene from the tomb of Rashepses, Vizier to the Fifth Dynasty Pharaoh Djedkare Isesi:
The hieroglyphic inscriptions above the players on either side of the board simply read hꜤa mHn or "playing Mehen".
The game of Mehen is discussed in some detail in a paper by Timothy Kendall (available as a pdf download from Academia.edu (registration required)). This paper includes the image of the game being played, from the tomb of Rashepses mentioned above, as figure 4.16.
A modern version of the game, with a board broadly identical in form, is called Hyena Chase. This game also originates from North Africa.