One can take this as the basis of a cosmic conspiracy theory (some sort of Argument From Design), explain it away from a biological science angle (Dawkins), or try to apply it from a physical science angle as the book wishes. Suppose for a moment it deserves comparison with the PrincipleOfSufficientReason.
The point in broad philosophical terms would be to get at the statement that there are 'states of affairs' in the world that are arguably arbitrary (just as for practical purposes there are contingent events). An AnthropicPrinciple could argue that they are arbitrary only within some limits. Go with the Leibnizian idea of 'possible worlds', and then see what sort of constraint Man - human existence - puts on a possible world. This is very schematic, of course.
In physical science terms, keep the structure of physical laws the same but allow variation in the fundamental constants, giving us a parametrised family of universes. What we are supposed to be doing is to describe in some outline way the set of universes in which human life could be found. The exercise will depend on manifold assumptions, for sure. We probably believe that a 1% change in the gravitational constant would be tolerable; but on the other hand slight changes in the chemistry of the water molecule might not be. Here scenarios from HardScienceFiction are played out. Of course a really well-posed question of this kind might fail to have an answer because the set of conditions was too hard to describe, in a way familiar from the complexity of fractals. In fact for refined questions of counterfactual type, such as 'would there be a Napoleon in this universe?', one might expect that to be the case.
There is no particular reason in mathematical terms to use real rather than Boolean parameters, though Leibniz was a couple of centuries ahead of his time in (apparently) intuiting this. SpeculativeFiction happily tackles questions like living off-planet in zero-g: in fact it's a staple to explore the possibilities. It would take one of the more thoughtful authors to try to delineate the human/alien boundary in terms other than scientific: if a high-g planet caused the inhabitants to be of small stature that would raise few SF eyebrows, but what if there were cultural aspects which seemed non-human?
The Barrow-Tipler book identifies an intellectual split at the end of the eighteenth century between the followers of Paley, the celebrated proponent of the Argument From Design, and the followers of ImmanuelKant?, on the question of how to handle the 'anthropic principle' area. Not a term used at that time, probably, and it is notoriously hard to summarise Kant accurately (I await the publication of Idealism for the Idle - All You Really Need To Know). The attractive humanist version of an AnthropicPrinciple would be that in practice you don't find minds, as we understand that term, in universes that can make no sense to them. That could of course be denied (existentialists seem to), be read as 'conditioning' by heredity (innateness) or environment (socialisation), or read from the mind to the universe (which seems to be Kant but don't quote me on that). For example we get linguistic theories of various kinds, the most celebrated being Chomsky's about innate parsing.
The looseness of the phrase 'state of affairs' seems to stand in the way of doing much that is clearcut with said principle: compared even with 'actions' of various types there is too much scope for loose talk, especially when it comes to social structures. Minds as we understand them do succeed in integrating the subjective and objective: the faultline between meaning and significance mentioned on the WritingAgainstLoss page is a rift that in practical human terms can be bridged. The sought-after AnthropicPrinciple that brings me to this point is really an inferred or hoped-for abstraction to do just that, communicably.