You'll need something on the Arduino that sends an event to your PC whenever the button is pressed. The easiest version of this would be the Serial channel over USB.
Second, you'll need a program running on your PC that receives that Serial message and generates your desired keyboard and mouse events.
In Windows, you can generate system wide keyboard and mouse events fairly easily using the Windows API. This would allow you to click a mouse, or keyboard button when inside of most programs written in Windows. https://msdn.microsoft.com/en-us/library/ms171548(v=vs.110).aspx
That said, you can have problems sending spoofed events to video games that don't use standard Windows forms. You might find this answer helpful from StackOverflow - https://stackoverflow.com/questions/7320424/c-win32-simulate-keypress-with-directinput