While we don't know the exact circumstances (were he and his wife separated, did she know about this "relationship," etc.), if this is how the wife found out about it, I feel very sorry for her. Such a discovery can be devastating and the wife should be able to choose how she handles it, who she tells, etc. Having it dropped like a bomb on her and her family is devastating.
That said, the reaction of the "couple" when they saw the screen was very telling, especially the woman's. She very obviously was caught! She quickly pulled away from the guy and covered her face in shame and embarrassment. They both made their own choices, and chose to act on those choices in a very public setting, complete with thousands of people, cameras, a huge screen, cellphone cameras and instant access to social media. They have no one to blame but themselves.