Squares

After about 53 minutes into the game, my game starts to lag and the floor becomes squares of different colors. What is this?

It sounds like your computer is getting bogged down with some processes of some sort. Many times background processes will "turn on" and will begin to slow down your computer. Also, it could be the GW servers, I've had times where it just flat booted me out of the game.

the squares could be what are called *visual artifacts* indicating stress on the card from possible overheating or overclocking OR it is on its way out

Sounds like your GFX Card is over-heating and generating artifacts. o_O

[EDIT]
Beat me to it Loviator...

[EDIT 2x]
By the way, what's your PC Specs? Graphics Card, Processor, RAM, etc? Although it is probably your GFX Card, also, driver versions of your GFX Card would help.

If you don't know how to get your specs, then;
Start, Run, dxdiag, OK - Info is there, then go on the 'Display' tab for your GFX Card information.

If you have an Nvidia grapics card then all you need to to is update your drivers. This is a known issue and it has since been fixed by Nvidia.

Actually in some case depending on what card it is, he might have to rollback his driver.

Just give him chance to post his PC Specs first please.