So perhaps a sore neck? I was just looking closely at the pics and penguin chick really does look awkward, it appears to have real trouble with neck and back, it certainly doesn't hold its head like the others. Know of a turkey chiropractor??
Speaking in human speak with regards a sore neck where bones are out of place, heat applied to the area would at least assist, as penguin chick grows could you (would you?) ever so gently stretch its neck? Not enough to kill it of course, but perhaps realign the bones IF it doesn't resolve itself. Maybe a few days and it'll be fine? Ethel should be giving it enough warmth to right any muscle soreness.
Lordy, have you ever had a stiff neck?? It bloody well hurts!!!!!