The Kansas City Chiefs do throw touchdown passes, just not to wide receivers.
A stat that almost seems unbelievable is that the Chiefs have yet to complete a touchdown pass to a wide receiver in 2014. In fact, it's been a calendar year since a Kansas City wide-out has recorded a touchdown reception. The last time a Chief wide receiver caught a touchdown pass was in a win over the Redskins on December 8, 2014. If you're doing the numbers at home, that's 17 games, 363 days and more than 1,000 offensive snaps without a touchdown pass to a wide receiver.
As stated above, Kansas City quarterback Alex Smith has continued to find other ways to complete touchdown passes. Nine of his touchdown passes have gone to tight ends, eight have gone to running backs and one to fullback. Tight end Travis Kelce and running back Jamaal Charles pace the Chiefs with five touchdown receptions apiece. Tight end Anthony Fasano has four touchdown grabs, while running back Joe McKnight has pulled down two touchdown receptions. Fullback Anthony Sherman and running back Knile Davis have each caught one touchdown pass from Smith this season.
Andy Reid's Kansas City offense is similar to the classic unit Marty Schottenheimer employed in the 1990s. The Chiefs are 30th in the NFL with an average of 196.7 yards passing per game, but with Smith at the helm, have thrown only six interceptions. The Chiefs bread and butter rests in their running game, with Charles and Davis combining to rush for 1,438 yards and 14 touchdowns thus far.