It's definitely nicer than most table service locations on property (think nice steakhouse), but park wear is acceptable. I wouldn't wear flip-flops and tank tops, but jeans are fine. The decor and atmosphere lend itself to dressing a little nicer, and just makes it feel more special IMHO. I usually wear pants or a skirt and a nice blouse or sweater.
If you are going for dinner, I personally would dress up a little bit. Nice blouse & slacks, nice shirt for the men. If going for breakfast, we were in our park wear and did not feel uncomfortable. But Like blackjack says, it depends on what you think nice park wear is
It is a nice resturant, and does lend itself to dressing up a little more then lets say goofys kitchen. Have fun the food is fantastic there, we went three times over chirstmas and did not have a bad meal and had great service.