This is ridiculous. It'll never stick in Europe, either. To make a trademark claim you need to be operating in the same sort of market, and you really need to prove that this restaurant is profiting from the popularity of Apple's brand by people confusing their logo/brand with that of Apple.

The latter is a real requirement in trademark law. It might be worded slightly different in the specifics, cause it's been a few years since I learned about it.

Another requirement for maintaining your trademark, is that you spend reasonable effort to protect it. That is, you can't trademark some word or logo and do nothing with it, and then when some other company happens to use it, grows big, you can't suddenly jump out of the shadows and say HAHA! I TRADEMARKED THAT (yes, that is indeed quite the opposite from what those software patent trolls are doing, patent law is quite different from trademark law, even though they both fall under IP laws).

In some strange and twisted sense, Apple's lawyers might have gotten the idea that this is how they should be protecting the Apple brand. Except Apple is not in the restaurant business, nor does the general public associate their brand with restaurants in any sense, so that's that.