Quotes from Google:

Basque people were present in Eureka, Nevada, particularly starting in the 1890s and into the early 1900s.
While Eureka is noted for its diverse population during the mining booms, including significant Italian, Cornish, and Chinese communities, Basque immigrants arrived later, mainly as enterprising sheepherders.
In fact, Basque descendants are described as one of the two most prominent bloodlines in Eureka today, along with Italian descendants.
Basque immigration to Nevada was often tied to the sheep industry, and many Basque communities thrived in northern Nevada, including areas like Elko, Winnemucca, and Reno.

Yes, Jai Alai is strongly associated with the Basque people and their culture. It originated in the Basque region of Spain and France. The sport, also known as cesta-punta, is a prominent part of Basque pelota, a broader set of traditional Basque ball games.
Here's why:
Origin:
Jai Alai's roots are firmly planted in the Basque Country, where it has been played for centuries.
Cultural Significance:
It's a deeply ingrained part of Basque identity and is often promoted as a symbol of Basque culture.
"Cesta" and Technique:
The distinctive curved basket, called a "cesta," used in Jai Alai, is a creation closely tied to the Basque region.
Players:
Traditionally, first-class players have come from the Basque Country, and training schools in the region continue to develop new talent.
Global Spread:
While Jai Alai has spread globally, it retains a strong connection to its Basque origins, with the sport and its terminology often reflecting Basque language and culture.