No, the blue law doesn't apply to restaurants, supermarkets, or gas stations that I can tell. I visit my inlaws up in Paramus often on Sundays because the traffic is less but the diners and such are open.
Rutherford, which has a nice down town area has some rules that don't allow restaurants to sell liquor/wine/beer. There is a cafe that has has a store inside of it, with a separate entrance at the street level, right next to the cafe entrance (think DC looks like its sort of inside Maryland). I think they have to operate as separate businesses, but basically everyone buys their wine there and goes into the cafe to eat.
Blue laws restrict the sale of goods on sunday. As stated above towns can choose to be more or less restrictive or not participate at all. Many towns in bergen county still restict purchases to essentials such as food and gas. It seems to stem from a time when the majority in the area participated in the "sunday is a day of rest" mindset.
As far as the Original question, restaraunts would be exempt from blue laws as far as I can tell since they sell food. I know some do close on sundays, but I would imagine that has more to do with lack of traffic generated due to surounding stores being closed.