That motherboard's onboard audio controller is more than capable of driving that headset; you do not need an amp.
Previous advice about front audio jacks is valid and worth ruling out; hardware and materials used to make and route those jacks are often of inferior quality, plus you have to deal with an extra cable and connector between your audio controller and jacks - which can alter impedance or introduce EMI.
Previous advice about disabling Nvidia HD Audio drivers is also important to follow.
Enabling Loudness Equalization can cause this same symptom when all else is working correctly, so make sure you're carefully testing that setting. It should generally be OFF.
Try Disabling "allow applications to take full control of this device" in audio device settings, if you haven't already.
Having a non-standard bit depth and sample rate set for a device can sometimes cause volume inconsistencies in games with poorly-implemented audio (there are many, particularly in the FPS genre). Try restoring to defaults.
You may need the Realtek Audio Console installed (packaged with motherboard drivers) to gain enough access to the chipset's low-level audio configuration for optimal functionality. Annoying when that's the case, but worth a shot.
With that said, that motherboard family does have longstanding known issues with audio quality, distortion and low volume on a wide range of audio chipset drivers for a lot of different audio peripherals. After trying all of the above, my next step would be to disable windows driver updates, uninstall the current audio driver, then reinstall the audio driver from your motherboard driver CD (or the earliest version available on the MSI website if you don't have one). If that doesn't work, I would try several different versions of MSI's audio driver packages from the same source if you haven't already. After that, try driver packages from Realtek.