What kind of machine learning is this?
This is supervised learning with a vector-valued output, i.e. learning a vector to vector mapping.  There's a large literature on this in the neural network community. One application is generating control signals for a physical device (e.g. pointing a camera based on visual input).  Here's a typical reference:    

Suh, I.H. and Kim, T.W. Fuzzy membership function based neural networks with applications to the visual servoing of robot manipulators.  IEEE Transactions on Fuzzy Systems, 2(3):203-220, 1994. 

From another angle, this can be viewed as multitask learning, a currently popular area in machine learning.   If one knows more about constraints among the output values, then it could usefully be viewed as a structured prediction problem, also recently popular.