Not really. The law isn’t specifically about video games. It applies to any technology considered an “electronic messaging service” or “advanced communication service”.
Strange. It seems kind of awkward for someone to use two devices to chat in a game. But I noticed upon checking that Discord is available for mobile too.
Not specifically for this law, perhaps, but the question itself is a good one, as there are a lot of different interpretation of what a game is, and those can definitely impact laws and regulations.