We were there in January and there were no chicken fingers or kids menu of any kind. Most buffets offer pasta, chicken fingers, mac n cheese, etc...but not the Biergarten. I had to find stuff off the "adult" buffet that DS would eat.
No chicken fingers. However, my DD has been going since she was, well since she was born, and it is one of her favorite restaurants. She finds tons of stuff to eat. The different sausages, hot and cold vegetables, and great desserts make her day.
I am the mom of one very picky eater. We asked the chef if there was something available for our DD. He suggested all of the things available on the buffet that were comparable to American food. Schnitzel (fried chicken cutlet), sausages (similar to a hot dog) and fried potatoes (french fries). Nothing our daughter would touch. He was very, very generous and personally went down to the American pavillion and got chicken fingers for our DD. Not sure if this is still possible as we haven't tested it in our last couple trips. It never hurts to ask. They can't hit ya.