If it just for disable during gaming sessions, just unplug it or if it’s a wireless mouse don’t turn it on. Those would be the simplest without having to change configurations setting every time.
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More information is needed. Probably it is a Windows tab. But not sure. Please share about its full configuration. Is there a shortcut for this? Is there a user manual?
Windows doesn’t have an option to hide the mouse pointer completely. The mouse pointer does exist and its by design.
Let me give you an instance why the pointer cannot be hidden completely.
Hovering your mouse pointer: Position the pointer to a specific object without clicking any mouse buttons and without moving for at least a second. Hover isn't supported by most touch technologies, so users with such touchscreens can't perform any tasks that require hovering. Lot of windows application does use hovering feature. This might be one of the reason that the developers at Microsoft did not include the feature of hiding the pointer.
However, there are some third party software that can hide pointers completely.
Third Party Disclaimer: Note: Using Third Party Software, including hardware drivers can cause serious problems that may prevent your computer from booting properly. Microsoft cannot guarantee that any problems resulting from the use of Third Party Software can be solved. Using Third Party Software is at your own risk.
It seems to be more of an issues with BIG FISH of not showing the cursor. More users complain about not seeing it. I'd check out and post in their forum.