It depends on how you count injuries. Our Adjusted Games Lost metric counts not just missed games but also players listed as probable, questionable, or doubtful on the injury report, adjusted for how often players listed in those categories actually played in games. So not only do we know who did and didn't play in each game, but who played hurt.
The Chiefs ranked 26th in AGL on offense and 13th on defense. So really, they had below-average health overall, but nothing historic. Yes, some key players got hurt, but it was nothing like the massacres that struck the Minnesota secondary (11 different defensive backs started at least one game) or the St. Louis receivers (eight wideouts got a start).
What's unique about Kansas City's injury situation in 2011 is not how many players they lost to injury, but how early in the year those players went down. The Chiefs had three projected starters (Tony Moeaki, Jamaal Charles, and Eric Berry) who were each inactive for 14 or more games. That only happened to three teams from 2000 to 2010. Then in 2011, it happened to Kansas City, Indianapolis, and Carolina. (New England almost makes the list, with Ras-I Dowling inactive for 13 weeks.) Carolina, in fact, had five starters out for at least 14 games each, and a sixth out for 12 games.
Now, there are starters, and there are starters. I don't know how badly Carolina missed David Gettis in 2011. The Chiefs lost studs. Tony Moeaki is not a Pro Bowler, but he's a unique kind of player most teams don't have (as we'll discuss shortly). Eric Berry was a Pro Bowl safety; our list of rookie seasons most similar to Berry's includes Roy Williams, Sean Taylor, Nick Collins, and Ed Reed. And then there's Charles, who finished second in our per-play rushing numbers in 2009 and first in 2010. That's their best offensive player, their second-best defensive player (behind Tamba Hali) and another guy in their top ten, each out for all or most of the season. And nothing like that has happened to a team this century.