1. Combine cubed chicken and tomato sauce; toss to coat. Cut each square of non-dairy cheese in half and wrap each piece around a cube of chicken. Wrap a dough round around each, pulling the dough toward the top and twisting it to pinch closed. Repeat with remaining ingredients.
2. Heat several inches of oil until hot, then deep fry chicken pizza pockets until golden brown, about three minutes per side. Let cool on a wire rack (or crumpled foil).