There are several ways that "gaming" can degrade your hardware. Heat, usage, and power drain to capacity can all cause damage or degradation of equipment. Some of it by design, IE a HDD only has so much use in it (typically) before it starts to have issue. This can sometimes happen slow enough that your OS will see it and pop up a notification, and often just dies. Gaming produces more heat within your system. Heat is the enemy of all manner of equipment. Often people have old or underpowered stock GPU within systems that can cause issue with both heat and power fluctuation.
To say that gaming killed the computer, well...maybe but due to multiple issues likely. To consider that this salesman has to dumb down his techo speak to make...