It is probably due to the games you are playing may not be optimized for the cpu/graphics chip inside the note. Also if the game is rendering at 1080p video, which the note can handle from what I have read, that will push the gpu hard as that is not it's native resolution.
Try turning the graphics settings on the game down a notch and see if that helps. PC gamers have to do the same thing if their video cards are pushing graphics that are too intense, and frame rate suffers, then the card heats up a lot.
The note is a phone first and a game console a distant 3rd or 4th. Expect it to get hot when crunching gigapixels like a desktop.
Also, remember the battery will discharge faster while playing graphically intense games because the gpu needs power from somewhere. Just one more source of heat.
So that makes the cpu, the gpu and the battery all producing heat, as well as the screen and probably the memory from data writes. Surprised the phone hasn't locked up on you, forcing a battery pull.
It's not wrong to fondle the s pen.