Harrah’s Reno Hotel and Casino will close after Caesars Entertainment Corp. said it agreed to sell the property for $50 million to a real-estate developer, which will turn it into a nongambling resort. The change of business plan highlights the growing challenges facing traditional gambling operators.

The 82-year-old Reno, Nev., casino launched the Harrah’s brand, and 17 casinos in the U.S. now operate under the name. Caesars and VICI Properties Inc., a real-estate investment trust spun off from Caesars in 2017, agreed to...