Add Bill Gates to the list of executives whose businesses have been ensnared by the Trump administration’s battle with China over technology and trade.

The tech tycoon and philanthropist said in an essay posted late last week that a nuclear-energy project in China by a company he co-founded called TerraPower LLC is now unlikely to proceed because of recent changes in U.S. policy toward China. That leaves TerraPower, which had been working on the China project for more than three years, scrambling for a new partner and uncertain...