Nope
Venison and other wild meats - from mamals in particular here - are very low in intramuscular fat. As a result, the meats from these animals is really very lean.
The malnurishment from eating venison was actually something that would affect any one who was restricted to a very lean all protein diet. for example settlers who used to get stuck in winter with nothing but lean game meats. I am forgetting the paper I read on this as part of a work review project a few years back... but the point is this. When FAT was higher they were ok - hence eskimos who can live months on end eating seals and some tribal people that eat almost all milk, blood (better than killing a cow... they are hard to come by in places) for long periods are able to be vibrantly healthy. If I had time now I would look in my files and find the paper so I had the correct terminology... if you go to pubmed.com (or gov) and search author names Cordain or Eaton - Eaton in particular and cross reference with nutrition you will find what I am getting at. Any way the fat allows you to not become sick from eating basically ALL meat. Basically allows you to temper the physical issues related to lots of protein.
Humans are super adaptable and able to be amazingly healthy on a lot of dietary patterns. So, to answer your question, the kids were chubs because they are not active enough and eat poor foods (likely lots of processed foods).