A "kick" is exactly what the word means. "Guts" means intestines, viscera, the body organs in the abdomen (belly).
A "kick in the guts" literally means a lick in the soft part of the belly. In addition to being dangerous and possibly fatal, being hit in the guts is disabling. It affects the nerve complex called the "solar plexus," causing the diaphragm to spasm and cause difficult breathing, as well as intense pain.
So, it is, literally, a completely disabling, sudden, painful blow.
To say that a story "hit you like a kick in the guts" means that it affected you in such an intense way that it seemed like a strong, painful, physical sensation.
A similar expression is "it hit me like a ton of bricks." (A ton is 2,000 pounds, i.e. about the same as a tonne).