FIG. 1 is a front, right and top perspective view of a baby dining chair showing my new design; FIG. 2 is a front view thereof; FIG. 3 is a rear view thereof; FIG. 4 is a right side view thereof; FIG. 5 is a left side view thereof; FIG. 6 is a top view thereof; FIG. 7 is a bottom view thereof; and, FIG. 8 is a rear, left and bottom perspective view thereof. The broken lines depict portions of the baby dining chair form no part of the claimed design.