The illustrated patch is an Inventory Control Device (ICD). It's basically a very cheap radio receiver that's used to prevent merchandise, books, etc. from walking out the door.
The two towers that flank the exit of the store are radio transmitters set to the exact same frequency as the ICD. Because the ICD resonates at the same frequency as the signal which the towers are sending out, the towers' electronics can detect the ICD when it passes between them. This sets off the alarm.
The illustrated ICD is deactivated by essentially crushing part of it by pressing it against a hard surface of the right shape. Those two white, almost-circles in the center are the things that press in and destroy the ICD making it no longer resonant at the same frequency as the towers. The towers can no longer detect the ICD after the cashier has neutralized it.
Bottom line: this system is based on radio transmissions, not on magnetism1.
Postscript - This discussion is about how the ICD works. It's not a tutorial on how to defeat these devices. Enough information is left out of this discussion so that anyone attempting to use this information to steal things would probably get caught.
1There is another system! An article in the back of the May 1997, issue of Scientific American, p. 120, says that there is a magnetic element to these devices. Is the author, Joseph Ryan, Jr., who is a V.P. for global source tagging at a firm which makes these things, describing a different system, or is he perpetuating a myth? Or am I just completely wrong? This determination is left up to the reader. I do note that this particular “Working Knowledge” section of Scientific American is not reproduced on their Web site.