[tgv]

Eye-hand coordination, sure.

But you've got a motley set of studies. The first study says "After they played a driving or first-person-shooter video game for 5 or 10 hr, their visuomotor control improved significantly. In contrast, non–action gamers showed no such improvement after they played a nonaction video game" (emphasis mine). Not toddler's games.

The 2nd article is not only about FPS, but it is very low quality and relies on self report without a control group.

The third article finds a correlation between strategic video games and self-reported problem solving skills and self-reported academic performance, while showing a negative influence from FPS on problem solving.

So I'd say: nothing has been proven, certainly not about toddler's games.

[loandbehold]

Most of the studies showing negative effects of screen time are also low quality and rely on self reporting.