Welcome aboard to both of you.
Addell, the theory works exactly as you explained it: If the amount of money is fixed, then if one person gains, someone must lose. That's simply a matter of arithmetic. So if the premise is true, the theory will work.
The reality of world economics, though, is that the amount of money is not fixed. Even artificial attempts to fix it by tieing it to a comodity like gold don't work because the quantity of gold in the world isn't fixed and the amount of other available resources is also not fixed. Both are constantly increasing and, for all intents and purposes, the total amount of wealth available is limitless over time. The reason the gold standard was discarded is because physical money is just a vehicle for transporting wealth and artificially restricting it limits how much wealth can flow around the economy, limiting how big the economy can get.
Aquamarine - good link. I learned a few things I didn't know about the gold standard (namely, the relationship with unemployment).