In above case only one choice is selected at a time which does not confuse the machine hence it is DPDA only. The grammar for which it is constructed is (a+b)* thus even $\epsilon$ is acceptd which is true in given PDA. It is called NPDA only when situation is for same input, you have push option and pop option like (a,a/aa) and (a,a/$\epsilon$) at one state only which is not a case here. So given question is already in DPDA.