Being on the phone during play is IN game activity. Concentrating on a device instead of what is happening at the table is a CHOICE. If that choice leads to making idiotic mistakes then start making better choices rather than blaming someone else for your own lack of focus.
No, it's not. Me saying my character is attacking a goblin is in game activity. Me asking the bar maid if she has heard about the strange cult is in game activity. Me talking about a movie or looking at my phone is not something that my character is doing. It's out of game. In game are the activities that your character does. Out of game are activities that a player does but his character does not. View it however you want, however. We obviously view this differently.
The phone activity, whether you consider it in game or out of game, was apparently important enough for the DM to have to mention it in the scenario of his original post. Maybe so important that he is more than happy to say that the players forgot about the ring and gauntlet when they sold the armor...."when they wanted to check the ring and gauntlets that I reminded them that it was all in the set [sold]" as punishment.
Maybe I should rephrase this for you since you seem hung on ingame/out of game. The DM punished the group of characters for the actions of a player, not character, on his phone.