IF a 3 dot vector and a 3x3 matrix can rotate, scale and transform things in a virtual 3D space, could you use a 3x3x3 matrix and a 3.3.3 vector to do something to the games sense of time?
technically you need a 4x4 matrix to rotate scale and transpose in a 3D space (with the bottom row [0,0,0,1] and last dimension 1 on the points (0 for vectors))
these are called affine transforms and can be easily applied to more dimensions (you just need a (n+1)x(n+1) matrix for points in n dimensions)
Most games don't use 4D matrices to represent elements of the game. The time "dimension" is usually controlled by some sort of timer call-back function. It's probably possible to do it with 4D matrices, I just haven't seen it. Of course, to store a complete time dimension for a game might take up a lot of space.