I don't think this is relevant to the notion that consciousness is a form of computation.
The assertion that consciousness is a form of computation basically means that the physical process that happens in the brain/body that we recognize as consciousness can be described in terms of a computational process. A consequence of this, if it is true, is that replicating the same computation in a CPU would make the physical process that happens in the CPU just as conscious - assuming that we had identified the correct computation.
In this theory, the thing that would be conscious would be the physical CPU, just like the thing that is conscious is a physical human brain/body. The computation is just an abstract description of the common properties between the CPU and the human brain/body. It's not relevant that we could also describe the process inside the CPU as being a completely different computation - the abstract model is only required to be able to build and program the CPU.
To go back to my mechanical door analogy: we create an abstract model of the computations needed to make a computational system open a door when a person is near. We use this model to create the computational system, and we see the door opening when a person goes near the sensor. Now, we can interpret the computation happening inside the system in many other ways - but that won't change the fact that the door opens when a person is near, in any way.
I am not claiming that any of this constitutes proof that consciousness must be a computation. What I'm claiming though is that the paper, and similar arguments, are not refuting the right claims, and generally have a misunderstanding of what "computation" actually means, and its relation to physical processes.