Are physical laws uncomputable in any type of computation (according to this article)?
The reasoning given in the paper is too vague to be of much value. The question whether laws of physics are computable cannot be decided by a philosophical discussion. It already takes some hard physics and math to even properly formulate the question.

Let me give an analogy. It is impossible to travel faster than light, right? But if I shine a laser at the moon and move it fast enough, the laser dot on the moon will move faster than light. So how is this possible? We have a contradiction in physics. Or do we?

It is easy to have a discussion about computability in the real world, or computability of the laws of physics, at the level of the previous paragraph. For instance, the very nice and seriously presented result on the Undecidability of the spectral gap is easy to misinterpret, because the devil is in the details. The actual experiment cannot be set up because it requires unrealistic conditions. If we approximate the experiment, then the theorem does not hold anymore. But this does not stop people from misinterpreting the result.

For a more reasonable account of computability of the laws of physics I recommend A computable universe, in which you can find discussions of many aspects of computability. If you are interested in computability of the laws of physics then the Matthew Szudzik's contribution The Computable Universe Hypothesis.

Personally I would say that the question "is the universe computable" is ill-formed, because this is not a falsifiable statement. The question "are the laws of physics computable" makes more sense, but one really has to be careful how it is phrased.