After careful consideration, I consider your point moot. Why must they be mutually exclusive? We are meant to have a modicum of leisure time, where we can relax and enjoy life. This person may have a very devout prayer life, and if he wants to spend some time playing Wii U in between sessions of prayer, why is that wrong? If this person chooses to use that time to play the Wii U, provided he chooses wholesome games, who are you to turn him away from it? While there are certainly video games that would be unwise to play, the Wii U offers many games that feature wholesome, family entertainment.
As I understand it, we are meant to live lives that conform to the command to “Pray without ceasing.” That does not mean we are meant to live 24/7 in constant, focused prayer, but to have a focus on God. Is the appreciation of something fun a detraction from God, or is it perhaps closer to the mark that appreciating every moment we have as a gift from God is a better way to fulfill that command? I think we should be living in appreciation of God’s blessings, and that can be done both in thoughtful prayer with our Lord and in the things we do throughout our daily lives.