Do I understand pseudo polynomial time correctly?
The running time for binary search that you quote applies for the so-called RAM model. I think that it is usually assumed that the machine words have size $\Theta(\log n)$ bits, where $n$ is some natural parameter like the length of the input.

For binary search, the input has size $\Theta(n)$, assuming that the array's datatype fits in a constant number of machine words, and so the running time $O(\log n)$ is logarithmic in the input size. The running time of the dynamic programming algorithm for knapsack is $\Theta(nW)$, but the size of the input is $O(n\log W)$ (in fact somewhat less, since machine words have superconstant size). This is not polynomial in the size of the input. However, if the weights are encoded in unary, then the size of the input is $O(nW)$ (again, actually somewhat less), and so the algorithm is pseudo-polynomial. It's a matter of encoding - whether you encode the weights in binary or in unary.