"You hereby acknowledge and agree that:
A. WHEN RUNNING, THE GAME MAY MONITOR YOUR COMPUTER'S RANDOM ACCESS MEMORY (RAM) AND/OR CPU PROCESSES FOR UNAUTHORIZED THIRD PARTY PROGRAMS RUNNING CONCURRENTLY WITH WORLD OF WARCRAFT. AN “UNAUTHORIZED THIRD PARTY PROGRAM” AS USED HEREIN SHALL BE DEFINED AS ANY THIRD PARTY SOFTWARE THAT, WHEN USED SIMULTANEOUSLY OR IN CONNECTION WITH THE GAME, WOULD CONSTITUTE A VIOLATION OF SECTIONS 1, 2 OR 7. IN THE EVENT THAT THE GAME DETECTS AN UNAUTHORIZED THIRD PARTY PROGRAM, BLIZZARD MAY (a) COMMUNICATE INFORMATION BACK TO BLIZZARD, INCLUDING WITHOUT LIMITATION THE ACCOUNT NAME, DETAILS ABOUT THE UNAUTHORIZED THIRD PARTY PROGRAM DETECTED, AND THE TIME AND DATE THE UNAUTHORIZED THIRD PARTY PROGRAM WAS DETECTED; AND/OR (b) EXERCISE ANY OR ALL OF ITS RIGHTS UNDER ANY BLIZZARD AGREEMENT, WITH OR WITHOUT PRIOR NOTICE TO THE USER.
B. WHEN THE GAME IS RUNNING, BLIZZARD MAY OBTAIN CERTAIN IDENTIFICATION INFORMATION ABOUT YOUR COMPUTER, INCLUDING WITHOUT LIMITATION YOUR HARD DRIVES, CENTRAL PROCESSING UNIT, IP ADDRESS(ES) AND OPERATING SYSTEM(S), FOR PURPOSES OF IMPROVING THE GAME AND/OR THE SERVICE, AND TO POLICE AND ENFORCE THE PROVISIONS OF ANY BLIZZARD AGREEMENT."
Forgive the caps, not mine.
I'm not saying they do see (or are able to see) what goes on with your computer, but the tou does give them permission to spy on the playerbase.