Rapid City is a relative newcomer to the ECHL; they were a member of the Central Hockey League (CHL) - of which the Arizona Sundogs were also a member - from 2008-2014. When the CHL disbanded in 2014, the Rush were one of seven clubs to move into the ECHL for the 2014-15 season.
The Rush's first year in the ECHL was a decent one; they made the Kelly Cup Playoffs, and won their first round series against the Quad City Mallards (another ex-CHL team), before falling to the eventual ECHL Champion Allen Americans.
The move is advantageous for home games; a plane flight from Atlanta (the major city to which Gwinnett is a suburb) to Phoenix is about 1600 miles, or about four hours. By contrast, a flight from Rapid City, South Dakota to Phoenix is about 800 miles, or two and half hours by plane.
Why does this matter? Because of the ECHL's status as a second tier minor league beneath the American Hockey League, the only realistic scenario in which an ECHL player would be called up straight from the AHL would be in a goaltender emergency.
Given Arizona's AHL affiliate is all the way across the country in Springfield, Massachusetts, it's conceivable that the Coyotes could quickly call-up a goaltender from Rapid City in the early afternoon off a game-day and still get them to the arena in time to dress.
The affiliation agreement lasts for only one season, so it remains to be seen if this is a temporary stopping point en route to a more geographically favorable affiliation agreement, or the beginning of a longer, more fruitful relationship.