DETROIT—Under pressure from U.S. auto safety regulators, Tesla has agreed to stop allowing video games to be played on center touch screens while its vehicles are moving. The National Highway Traffic Safety Administration says the company will send out a software update over the Internet so the function called “Passenger Play” will be locked and won’t work while vehicles are in motion. The move comes one day after the agency announced it would open a formal investigation into distracted driving concerns about Tesla’s video games, some of which could be played while cars are being driven. An agency spokeswoman says in a statement Thursday that the change came after regulators discussed concerns about the system with Tesla. The first update went out Wednesday as part of Tesla’s holiday software release, and the rest of the vehicles should get it today. The statement says NHTSA regularly talks about infotainment screens with …