The cat command is not causing the change that you are seeing in the array shape. What's causing it is the fact that you are indexing with 3 subscripts (:,:,:) instead of 4. Since the cat command only receives 2 arguments it simply returns the 2nd argument unchanged. You could have equivalently generated var2 without cat as follows:
var1=rand(326,377,31,9);
var2=var1(:,:,:);
whos var1 var2
To do something meaingful with cat(), you must give it 3 or more input arguments, e.g.,
var1=eye(3); var2=rand(3);
cat(1, var1,var2) %cat along dimension 1
cat(2,var1,var2) %cat along dimension 2
cat(3,var1,var2) %cat along dimension 3
