This puzzle appeared in Microsoft Intern PuzzleDay 2007, whose theme was Harry Potter.
Traditionally, each participant in Intern PuzzleDay gets a T-shirt,
which is one of the puzzles. This was the T-shirt puzzle for 2007.
Since you don't have the T-shirt, you'll have to use other means to determine what it would look like if seven people, each wearing the shirt, laid down and followed the Twister-style rules given.
The seven people's positions should be reminiscent of a seven-segment LED display.
You may notice a lot of three-letter sequences that appear in multiple names.
Since it's an invisibility cloak, being active means your LED display segment is off.