Earlier quoted context omitted.
I'm not saying faces aren't determined by hereditary factors, only that there are also other factors. Almost all of the 'identical' twins I've seen had subtle differences.
Yet those differences are, as you said, subtle, that is, very small. That means that, in the context of this article, there is no huge range of faces we can determine from genes, but the genes (when we know them) actually determine the face very very precisely as proved by identical-twin-resemblance. The predicted faces in the article are fuzzy not because environment has a great impact but because our knowledge of t…
The differences between twins who grew up together and were exposed to the same environmental effects were subtle, not necessarily so for the difference between a person and a prediction based on their genome. The comparisons of predictions to real faces from the article showed that (so far) predicted faces miss tons of little details that make people recognizable. Genes do not work in a vacuum, different environmental factors can trigger the use of different genes, and many genes are expressed to varying degrees depending on chance. Say one twin grows up in a nutrient-rich environment while another grows up in a nutrient-poor environment. The nutrient-poor twin will most likely have more developmental issues than the nutrient-rich twin, which can have a wide variety of effects. Perhaps a model trained on more data would be more accurate, but I'll believe it when I see it.