Will the Pharaoh game from Gogo run on the Windows 8.1 OS (64 bit)?
I have a Microsoft Surface Pro tablet, however it's laptop specifications though with Intel i5 dual core, 4 GB RAM and Windows 8.1 64 bit OS.

Tablets are tablets, this game won't work on them. Even if you could get it working, you would find it extremely difficult to play the game, because the game expects a mouse and keyboard.

Ok, to make the question simpler, will the Pharaoh game version from Gog.com run normal in Windows 8.1 x64 bit operating system?

The game will work on Windows 8, but not on a tablet. It needs to be an actual desktop computer with a keyboard and mouse, not a touchscreen device (the game was made well before touchscreens existed, so it will not recognise them)

Well I installed the same in my Microsoft Surface Pro running Windows 8.1 x64 OS.
The only issue with the touch screen option is that it does not have the equivalent of a right click which will be recognized by the game, understandably as Shukaku mentioned, since the game was pre existing to the touch screens. Also you have to double tap instead of the single left mouse click. Otherwise the game works fine.

The Surface Pro is powerful as most of the laptops in market and also has the option of attaching the touch keypad with integrated mouse track pad. So all is well and you can play as you play in a normal desktop or laptop. I just completed the first game of basics and it's like reviving the old times. Thanks for all support.