There may be a "trick" to this, depends on how those two headphone systems are connected. I suspect the cheaper gaming set is NOT plugged into a jack on your sound card. They may be plugged into a jack on the back panel of your mobo, or into a socket on the front of your case, or they may be part of some sound system that plugs into a USB port. You should tell us that detail.
The "trick" part is due to a limitation of Windows and you can deal with that easily. No matter how many different hardware devices your system has installed for sound, Windows can use only ONE of them at a time for sound playback. Similarly for sound recording, only one device can be used at any one time. Go into the configuration tools for Windows to where you...