The line-out and the mic-in work on different "voltage" levels. Feeding a line level signal to a mic input might cause overloading that input. Some onboard audio can be reconfigured, in order to switch the mic-in to line-in level. In such case, there is no overload.
Can you elaborate more on how a USB headset would fix my problem?
An USB headset works like a second sound card and is recognised as such by the operating system. In many games, this second soundcard can be configured to be used for in-game-communication. Check the documentation of your games if such options exist.
Also, the mic from the headset is closer to your mouth, so there is less "game sound" when you speak to others. And you can speak to your game friends while recording the game sound with your onboard audio system.