Can playing games on your iphone a lot damage the phone in any way?

Not any more so than any other constant use of the device.

Games are no different from any other apps as far as battery usage, wear & tear on the device, etcetera.

Why do you believe this is a possivility?

It may fry your brain but it should not hurt the phone. Depending on your use, you may run out of power faster.

Granted, playing Candy Crush has a higher possibility of inflicting intentional damage to your iPhone due to increased frustration than using, say, the Contacts app.

Or Flappy Bird... that's an iPhone-thrown-across-the-living-room game if I ever saw one.