He is not merely a veteran - he is a veteran of World War II. In other words, one of the very few surviving members of "the Greatest Generation." That is, a generation of men and women deserving of our respect - not only for what they contributed to our nation - but to the entire world. In short - it is relevant, in every way. This man has earned the respect that he is rightly due. His sacrifices for his country should at the very least afford him a few extra minutes in "the iconic" American restaurant.
With no disrespect to those in the Greatest Generation, I see few reasons to afford a 'veteran' any special treatment that I would not offer to any other person in their eighties/nineties. Just being a veteran is in my opinion, no special reason to sanctify someone. In addition, many people assume veteran = served in combat when a 'veteran' may have served as a non-combat supply clerk; so to assume great sacrifice just because he is a 'veteran' is in my opinion also misguided (though supply clerk is also an important job).
Now don't get me wrong, because I am very grateful for what veterans have done, and there are many out there who have sacrificed for the benefit of others, willingly or unwillingly. But to automatically accord someone special treatment, over and above the usual high standards that should apply, simply because they are a 'veteran' is in my opinion not the best way to do things.