Is video considered a Tensor? A sampled single dimensional signal is a vector.
A sampled image is a matrix.
Is video considered a rank-3 tensor since it is a set of images stacked on top of each other?
yes - a video signal would be considered 3rd order tensor. 

scalars are 0-order tensors, vectors are 1st order tensors, matrices are 2nd order tensor,  data volumes are 3rd order tensors and so on for multi-dimensional arrays.