I'm surprised they managed to find a whiteboard pen which didn't destroy their display. Most of them have solvents which I would expect to interact poorly with the surfaces of LCD monitors.
That's the smartest part of the hack I guess - that the waiter actually invested time to test out his idea! Who knows probably the first marker he picked up didn't work the way he expected and he moved on to the next one till he found what worked.
My experience with generic "Don't put this chemical on that surface" issues has been that it usually takes quite a long time of heavy contact before there's a noticeable effect. I'm guessing an Italian restaurant with an identifiable "head waiter" can afford to replace a $200 monitor every few months.