Interior design is about creating comfortable, beautiful and functional spaces.
First, make it relaxing: Pay attention to color, specifically - and try to keep it warm and light. If it's just a media room, of course you'll want it dark. But we're not talking about just a media room. We're talking about a place where your family meets and relaxes together. Keep it light and friendly.
Have functional furnishings: The furniture in this space should be very usable - seating, games (like pool tables or darts), wet or dry bars, coffee tables and places to sit, relax, drink and engage one another. Keep furniture to proper scale for the room. Guests and occupants will need ample space to move around the room.
Where to put.... your family pictures and memorabilia? In the game room of course! Adding family photos and memorabilia as parts of the decor add a sense of nostalgia and warm family tradition.
Keep it neutral: Accessorize with things the family might use: a throw blanket, comfy soft pillows, a nice big-screen TV and refreshment/bar area.