I found the article you were referencing and also watched the ending of the Mary Tyler Moore Show on Youtube which the quote was about. I believe they mean it literally. In that final scene, they all hugged and then shuffled out of the newsroom. To shuffled out of a room, etc. means that when you walk out of the room, you do it in a very clumsy manner. For instance, by not picking up their feet as you walk and not walking out in a nice organized line, etc. It was very relaxed and clumsy. Here is the video: https://www.youtube.com/watch?v=YZZvTaFUKMQ The scene is at 23:30. CRANE: The finale for The Mary Tyler Moore Show, as they shuffle out of that newsroom, is just so fantastic. That they won’t leave that hug – that was brilliant.

Is it The Mary Tyler Moore Show? The cast is all in a group hug and they maintain the hug as they move as a group. To shuffle is to walk with small steps without lifting your feet very high off the ground. See minute 11:00 here: https://www.youtube.com/watch?v=8XAo6U9dD2g However they don't shuffle out of the newsroom, they shuffle over to the box of tissues. The walk normally out of the newsroom.

They leave the newsroom (where the TV series is set). It's not a confident or strong style of departure... just a shuffle.