Your reasoning is solid, but I have to explain a little more. I may have been using a wrong word. "Processing" sounds too much like only CPU calculations, while I meant it as a whole, CPU calculations, reading of the data and writing the data back to the database too. That part, the SQL database input/output is what takes the longest by far. So, copying the data to another server would not actually help since it would still need to read and write the same data, just like it does now.
Also, because this is a live site, to copy the data and then write it back, we'd have to be sure nothing changed it in the meantime. That itself would be almost impossible due to the volume of the code.
the game calculations take datas from SQL/Oracle tables and as result, they fill in another tables.
They often do that, but also they update the same tables they read from.