Programming multiple games on the 16F684A chip can be done but it requires that you use relocatable code not absolute code. It is also very difficult because the 16F648A has progam memory page boundries which require that you use the "pagesel" directive and might possibly need to modify the linker script.
The linker script tells the program where to find all the codepage addresses, databank addresses, etc. (it's simply a map of the PIC's hardware).
If you are interested in finding out more about relocateable code, here is a really good set of tutorials on PIC assembly level programming: http://www.amqrp.org/elmer160/lessons/
He uses the PIC16F84 but that shouldn't matter as all the information will apply to any 8-bit PIC.Lesson number 16
takes an in depth look at using relocateable code when you write your programs. All of my programs in assembly now use relocateable code.
My suggestion is to go through all of Brad's tutorials first (if you haven't already done so) because Brad explains it like no one else can! Then go through the lessons I just posted the link to. All of the lessons are in PDF format so you can save them to your computer and go through them anytime you want. He starts at the very beginning, from explaining the PIC architecture and installing MPLAB, to writing code for LCD's and other stuff.
You should have plenty of knowledge by the time you get through all of those lessons to do anything you want with the 8x8 game! If you really want to stick with PIC assembly then I highly reccomend this course. I personally have not found a better course to learn from.