Style? Most likely a simple "After Action Report" that simply gives mission details and tells of how I did certain things within the game, but in a concise format that may seem a little truncated to the average reader.
The game I'd do one of? Most likely one of my myriad military shooters, though I could easily do one in that style for Fallout 3 or any of the Mass Effect games. Could even do one for any of the aerial combat games I've got.
It would be typed out into a forum thread, not posted as videos. Reason being that I don't have a capture card.
Matter of fact, I think that if I hook up that Turtle Beach Earforce XP500 headset to my PS3, I'd be willing to do a coop campaign as part of someone else' LP, if they were willing to do Lost Planet 2 or Borderlands.