Can playing games damage a laptop?

I have a Lenovo Flex 2 15 (GeForce 840M, i7-4510U CPU @ 2,4GHz). It doesn't run most games at 60fps but I don't really care about that. What I was wondering, though, is whether playing these CPU heavy games can damage my regular laptop or not.

Playing heavy CPU games won't damage your laptop

Some CPU intensive games may overheat the laptop, thereby causing automatic shutdown of your laptop - in order to prevent melting down of hardware components

It is all about heat. No excessive heat, no damage. Excessive heat will do it in, so you should use a very good cooling pad and you must be able to track the temperature. You know you can't lay a laptop on a soft surface that prevents airflow (such as a bed or pillow) . There's nothing about it being a game that is harmful, it is the heat caused by the demand on the graphics by some games that is bad.

Why would it destroy a laptop but the heat that is created from playing might destroy the laptop so get coolers for the laptop and start playing

NO. Games create heat than the other things. But your lap is quite capable of handling it, unless you prevent the air control underneath of the lap by putting a cloth or something under. Do not put it on the bed either. Make sure your fan functions well and the dust isn't blocking the air flow