Julie answered the question pretty well in her comment, certainly with respect to precision. In terms of gentleness, to me, it could perhaps suggest that the animation is smooth, and not jerky, or perhaps that the colours are not garish. I think Julie was also quite right that it is very open to interpretation - I think the phrase is meant to give a general idea, rather than meaning anything specific.

animation is how something is drawn, precise is accurate or clear. so I would imagine that in this movie the animation, whether by drawn by computer or by hand, is accurate, and clear without harsh lines. It could also be speaking of how the characters are portrayed through the animation. "Gentle precision being, not creating dialogue that makes characteristics too unbelievable. You have to speculate or infer meaning with this selection....someone else could see this as totally different.