No, there is no pseudo-science there, except when one takes the statements to mean more than they actually mean.
>Any correspondence between formal properties of the algorithm, namely, the logical model of the system and its physical properties requires (1) the algorithm; and (2) the implementation model.
>Speaking about "computational processes" and "reversibility" at all, absent these, is meaningless.
This is simply not true. We start from the assumption (as does all theoretical CS) that computational models are equivalent in capability.
We observe that the brain has inputs and outputs. We observe that the outputs are at least partially determined by the inputs.
From this, we can conclude rigorously that the brain does computation, and there is thus a computational process going on in the brain.
>What exactly, of the brain is the "computational process" ?
The correlation between inputs and outputs that follows a process in which information is transformed. This is readily observable.
>What exactly is "irreversable" ?
It is impossible to reconstruct the input from the output, therefore the computation is said to be irreversible, and is thus subject to various thermodynamic limits.
Therefore, we can rigorously conclude that the brain performs irreversible computation.
>We have no idea whatsoever what a logical model of anything to do with animal intelligence is, and hence, absolutely no idea what properties of animals (local to the brain or otherwise) are relevant to them implementing this logical model. To say any process of the brain is "computational" is either to say something useless (namely in the sense in which every process is "presumably, somehow computational, given a logical model") -- or, to say something pseudoscientific.
Now you're just taking what I said far above and beyond its actual meaning, and taking that interpretation to be pseudo-scientific. I said nothing about intelligence, all I'm saying is that there are computational processes going on inside the brain, and that those are irreversible. We don't need to know what algorithm is going on, nor do we need to know the precise model of computation, to be able to draw conclusions.
One of the conclusions we can draw is that the brain executes irreversible computation, and that the general algorithms implementing those computations must not be zero-work.
That is done without needing to know the details you seem to argue are necessary to draw such a conclusion.
We can also conclude more from this. We can, for example, place lower and upper bounds on the information being processed by various elements.
Now, someone could take this methodology and abuse it, or, as the article does, use it in conjunction with supplementary assumptions and go beyond absolute rigour.
>If the whole of reality is an algorithm, it's one (via energy conservation) which requires zero energy to run. Ie., "logical bit" and "thermal bit" are radically different notions. They are connected contingently when one has an algorithm to-hand, and knows how it will be implemented.
Now you're going way beyond what we can rigorously ascertain. If you consider the whole of reality to be a computer, then what are the inputs, and what are the outputs? Perhaps you consider the process of time to be an algorithm with the past as an input, in which case it is an algorithm that does require energy to run because it's performing irreversible computation, unless there is hidden state somewhere.