To me, the issue and flaw with this argument, as with most computation-based theories about existence and consciousness, is that we like to conceive of computation in purely abstract terms. But it's been known since the 1940s that the concept of computation is founded on information theory, which is simply a restatement of parts of the laws of thermodynamics, which are derived from classical physics and applicable only in the macro world.
But we know that the universe is not classical in nature. So it seems to me that trying to use a classical-only approximation to do all the backfilling to a theory of the nature of existence must necessarily come up short. It feels "like butter scraped over too much bread."
Information theory also establishes that any information state must correspond directly to a physical state, so it seems to me most likely that all our concepts of mathematics are not communions with the mind of God, but projections of some aspect of the physical functioning of our brains. And since our brains are products of a non-classical universe, the classical nature of our concepts of computation represents some sort of essential reduction of complexity; just like our brains reduce the complexity of our sensory inputs to produce a model of the world sensible enough for us to act on. Trying to employ that reduced-complexity model to account for the nature of existence itself is necessarily forced and futile in my view, like trying to explain the nature of a reflection in a mirror as an alternate dimension.
It reminds me of how Frank Tipler pointed out that Nietzsche's theories of physics and his concept of eternal return were in fact formally correct, or would be if the universe were classical in nature. But the universe is non-classical, and thus there were surprises in 20th century calculations of the nature and destiny of the universe.
Until there are full non-classical theories of physics and of computation, I think we as well will need to expect surprises in conceptions of how existence came about.