When does a photograph of a person become a portrait? According to Wickipedia it should be an artistic representation of a person where the face and expression are predominant. It should show likeness, personality and mood of a person. The person normally should be looking directly at the camera so that he subject directly engages with the viewer. 
If you look at the first photograph it fills the criteria. It is well lit, clearly you can engage with the eyes whch is so important. I do think that the cocept of a portrait has cahnged and only part of the criteria needs to be met. Particularly with child portraiture you can show much more of their personality with action shots. I do think that it is easier for parents to relate to.
The second photograph clearly doesn’t fulfill the criteria but is it any less a portrait? My view is that the most important aspect of a portrait is that it should reflect personality. Now children tend to be full of energy and fun and I believe that this is reflected in this photograph. You can see this without having a clear view of her face or eyes. If showing personality is the main criteria then both photographs fulfill the role, both sets of parents are happy with the results for different reasons.













