I’m not sure about American colonists, but Spanish conquistadores and missionaries record many instances of games played by the indigenous peoples in central and South America.

The Spanish were a very legally oriented society by the time of the the conquest so they left a wealth of historical resources.

The instance that comes immediately to mind is the Incan king, Atahualpa. Basically Fransisco Pizarro arrived in Peru during a war of succession after the death of the emperor. It was Pizarro’s 3 expedition to conquer to Incan empire.

During a meeting turned engagement Atahualpa was captured. He promised the Spaniards a ransom of a 20x17x8 room filled half with gold and then twice with silver. The ransom was paid, but Atahualpa was not released. During his captivity Atahualpa taught some of his captors the game of “Perudo” an ancient Incan gambling game. Atahualpa was strangled after a phony trial. This was hastily done by the Spanish who believed a large Incan force was in the way to engage them.

The other example I can think of is Ulama, which was played throughout Mesoamerica. It involves keeping a rubber ball airborne and scoring through a hoop. There have been over 1500 courts found, so we know the game was common.

The Spanish accounts relating to Ulama are characterized by an observational role. The Colonial Spanish administration sought to suppress the game due to its religious and ritual significance.

I am not aware of any instances of Spanish playing the game, but indigenous people who were brought to Spain did demonstrate Ulama to Charles V.

At the time of first contact and for a period after there was staunch debate on the status of the indigenous people. European ‘visitors’ were not sure how to categorize them. They literally debated their humanity. Of course, the indigenous peoples of Latin America were violently exploited throughout the history of Colonial Spanish America.

Indigenous games were most likely seen as fascinating, but partaking in said games would have been seen to lower oneself to the level of the perceived ‘other’.

There are also plenty of examples of ‘intermarriage’ of european men and indigenous women. Often the result of sexual violence. This resulted in the creation of the Casta System, but that’s for another time. The point is that there was a mixing of cultures going on during the conquest period. The Spanish altered Indigenous culture to be acceptable to themselves and still palatable to the indigenous. This is true with everything from religious services to games. At the same time there was a harsh moratorium on all things thought to be a threat to the Spanish Administration or the Church.

The answer to your question is that it did happen. The more complex answer is that it was rare in Spanish society and was probably relegated to poor lower casta people. It was also probably more prevalent in rural areas.

Edit: I hope this answered your question, I wasn’t sure what you meant by “American colonists”. Let me know if there’s anything I can clarify