Adverse health effects have been observed among children with a functional but unused oven or stove such as higher rates of diabetes and asthma and other life-long effects.
Well, we can think about why, and try to to minimize risk.
If it's unused, and they didn't control for diet, then it could be that they're eating processed foods. I would be extremely interested in seeing the diet of a family that didn't use a range/oven, and the relative amount of phthalates and the like.
Assuming they are getting good quality food, then an old stove will always have a pilot light on, even if it's unused. I think it would be hard to ventilate the emissions from a pilot light, since most ducted vents have flaps that only open when a fan is on. But...
If it's a modern stove, then an unused gas stove is the same as not having a gas stove at all, since there's no pilot light, unless you have a gas leak.
In my case, I have a modern stove, and no gas leak (it was tested), so I think my situation is probably different than whatever study you have in mind, assuming everything is properly ventilated while it's on.