The answer to the question is, well yes, we could be - but that is not what this book is about!
The premise of Seth Lloyd's excellent book is that, like 'energy', 'information' is itself a fundamental physical quantity. Energy, as any physics student knows, makes everything happen - but what is it that determines exactly what happens? The answer is information. In a real sense, the Universe is a giant computer that is constantly processing information.
But this is not some fanciful science fiction plot and the author is not suggesting that we are living out the storyline to "The Matrix" (although we could be). It's just that, in the 20th Century, as more was learnt about the nature of matter (quantum physics) whilst, in parallel, a method of high-speed processing of vast quantities information was developed (computing), physicists came to see how the processing of information underpins activity in the structured universe. This is a very serious topic indeed and, if you've introduced yourself to the ideas behind quantum theory, this book is great way to develop that understanding a bit further.
Like all good popular science books, "Programming the Universe" is aimed at the general public like you and me - you don't need a science degree! The author uses easy to follow analogies to explain all the complex theories. There is a good narrative thread, plenty of humour and it is entertainingly written. The early chapters explain the 'computational universe' - how much the universe is akin to a computer. We then go on to learn how quantum particles can and do behave like the binary 'bits' in a microprocessor - the ones that are either a '1' or a '0' - and how it is possible to use them to perform logical operations, just like the chip in the PC on which you have accessed this page. The difference is that quantum bits don't have to be in one or other of the two mutually exclusive states (i.e. '1' or '0'), because, as we know from quantum physics, particles can simultaneously be in two states at once. There isn't enough room here to explain why (you'll have to read the book) but what this means in practice is that a quantum computer would do many things at once - such as performing a search in multiple places or factorizing a prime number by computing all the possible factors simultaneously. In short, a quantum computer will be an order of magnitude more powerful than our current classical machines.
There is a very thought-provoking conclusion about a quantum computer that could simulate all the processes in the universe from the big bang to now. We don't know who would build such a machine or why they might do it but we do know exactly what it would look like and how long the computation would take. I shall say no more.
Needless to say, I disagree with the initial reviewer's comments. The computational nature of the universe isn't just plausible, it is fact. And treating information in the same way we have been classically doing with energy, i.e. as a fundamental physical quantity, opens up a new way of thinking about the universe. Amongst other things, it can explain how complexity arises out of simple particles of matter. The idea of information as a physical thing may seem abstract and difficult to grasp but it is worthwhile. There is no claim in the text that the universe is actually a computer - it just behaves like one.
As a small aside, there is no complicated maths but I would recommend that you are 'up to speed' on some of the very basic tenets of classical and quantum physics before you attempt this book - 'A' level stuff. I say this because I would imagine that the text might not be so rewarding if you had to rely solely on the quick analogies used here to describe things like entropy and wave/particle duality (though I may be wrong - you might be a faster learner than myself). Also, a little knowledge of what goes on inside a microprocessor (c.f. logic gates, memory registers) might be helpful!
To sum up: thoroughly entertaining and seriously thought-provoking stuff.