Suggestions for a solution: still not sure about the source or origin of the problem.
With a four year old keyboard it may simply be at EOL (End of Life) as designed...
You could try new batteries and/or move the USB receiver "closer" with a USB extension cable.
However, you would likely be having far more "keyboard" problems than just the key presses you describe.
Another consideration would be some key press remapping via game software or a utility.
But again, I think you would be having other keyboard issues as well or be aware that the key press combinations had been remapped. (Barring some buggy update or utility.)