The Entertainment Complex, together with the Arena, is a very much forgotten piece of infrastructure, as the only situation in which anyone would want to build it early is when they want to construct the almighty Colosseum. (In vanilla Civilization VI, the Arena is not required for the Colosseum.) For the Aztecs, the conquerors of the world, there is definitely no reason for them to have to build this Wonder when they can take it forcefully instead. The Tlachtli is obviously an upgrade from the Arena, but its bonus is nowhere near enough to warrant an early focus. 2 extra Faith is too small, especially since the spoils of war will always be much greater than this, Amenities are supplied in much more generous amounts by Luxury resources and the Aztecs always build at least 1 or 2 Encampments for some Great General points.
Overall, this building is one of, if not flat out the worst piece of unique infrastructure in the game, as it gives some bonuses that the civilization either does not need or can obtain in abundance easily from another source. In the vanilla version, you can pretty much ignore this building entirely, or at least delay its construction until much later in the game when Amenities are required to support larger cities. From Rise and Fall onward, if you capture the Colosseum from a neighbor, the standard Arena required to build it will be converted into a Tlachtli afterwards, giving you both the Wonder and the +4 Era Score, as truly under almost no circumstances would you ever want to waste Production on this building.
For over 2700 years the Mesoamericans played their traditional “ballgame” – Ollamaliztli in Nahuatl – in (not surprisingly) “ball courts.” Somewhat similar in play to team racquetball, these “sporting events” had significant ritual overtones, given that the losers (and sometimes the winners) were often sacrificed after the game, usually by decapitation. Explicit depictions of human sacrifice after a game can be found in many Mayan ball courts such as those at El Tajin and at Chichen Itza. Although the sport had somewhat different rules in different places and different times, it spread throughout Mesoamerica, as far south as Nicaragua and north as Arizona. Built in a pattern that changed little over two-and-a-half millennia, the ball courts were stone constructs of a long, narrow playing field between high sloped walls with open-ended (later enclosed) wider goal areas. Painted and decorated, these stadiums were the epitome of the Mesoamerican civilization … until the Spanish showed up and introduced the natives to other games.