Perhaps Shafer-landau feels justified in being dogmatic at points, and in offering less than convincing arguments against his interlocutors, because he defends the subjects in the book in greater length, and in a much more detailed and rigorous fashion in his Moral Realism: A Defense. He asks, "Why think morals need a lawgiver when you don't think any of the other 'laws' in the universe, e.g., gravity, need a lawgiver." However, and quite apart from the various responses and moves theists can make here, I'm not sure I wouldn't say that his question involves another argument for God's existence.
This book, while an introduction, is not a typical survey consisting of a presentation of the central topics, with arguments pro and con; rather, Shafer-Landau uses this introduction as a means to argue for the objectivity of morals. Throughout the book, he makes a case for moral objectivity, all the while considering various counter-arguments and objections to moral objectivism. While Shafer-Landau uses this introduction to make an argument for his own philosophical views, it is uncharitable to accuse him of being opinionated or biased. Instead, Shafer-Landau thinks he has a good case for a certain view, so he presents a good argument for that view. Either way, Shafer-Landau does little to engage the views of other contemporary metaethical theorists. Substantively, this book covers a lot of good information that will most certainly disabuse the reader of vague conceptions, fallacious arguments, and incomplete notions about a number of issues. A careful reading of this book will give the reader a strong sense of how to argue about various issues concerning moral objectivism.
In Whatever Happened to Good and Evil Russ Shafer-Landau tries to rescue moral objectivism (the idea that certain moral judgements are indeed objectively correct or incorrect, always and everywhere, and independently of who utters them or what culture they come from) from a variety of forms of moral skepticism: nihilism (the idea that moral judgements are meaningless or refer to nothing at all), moral relativism (the idea that moral rules are social conventions, like the rules of grammar or of baseball), and moral subjectivism (the idea that moral judgements are personal evaluations, like disgust or erotic attraction, and are only true or false to the extent that they are sincere or insincere). 2. Any form of moral objectivism can be logically disproven. This form of logical argument, though, at best only demonstrates that moral objectivism remains logically possible it doesnt actually make a case for it being true. (Though Shafer-Landau has written a larger book, Moral Realism: A Defence, that may make this case: I dont know.) So in part one, he describes a number of arguments for moral skepticism and shows that they each have weaknesses that make them unable to successfully win the day.
Shafer-Landau offers a brief defence of a non-naturalist form of moral realism. Is Shafer-Landau begging the question? Here, Shafer-Landau offers positive arguments for moral realism. As many of you will have already guessed, Shafer-Landau thinks that moral knowledge is very much within our capacities and is entirely a-priori (similar to mathematical knowledge).
This is a short and sweet summary of meta ethics and an argument for the status of moral claims being objective.