Why is incomputability weaker than Kolmogorov complexity?

Abbot et al. "Experimentally probing the algorithmic randomness and incomputability of quantum randomness" remark that "incomputability is a weaker property than Kolmogorov randomness". I understand that a Kolmogorov random infinite sequence is incomputable. The statement implies that there are incomputable sequences that are not Kolmogorov random. Why? (It's difficult for me to imagine what such a sequence would be like. If the answer is complicated, pointers to textbooks or literature at a similar level would be welcome.)

Take your favorite noncomputable infinite binary sequence $$f$$ and consider the new sequence $$g:=f(0), 0, f(1), 0, f(2), 0, ...$$ Clearly $$g$$ is again noncomputable ($$f$$ and $$g$$ have the same Turing degree), but $$g$$ also has lots of "predictable behavior" since every other bit of $$g$$ is zero. This prevents $$g$$ from being Kolmogorov random. So, in fact, not only does noncomputability not imply randomness, but every noncomputable sequence has the same Turing degree as a non-random sequence.