What Diamond is saying is that treating the study of history as a science will make history a more objective and more useful discipline.
According to Diamond, historians could do a better job if they would use natural experiments to try to analyze major trends in human history. He realizes that it will never be possible to make history as "hard" of a science as physics or chemistry. However, he thinks that it would be possible to discern broad trends and to make general predictions about the future. If historians would look at "natural experiments," he argues, history would be more objective and would provide better insights into the human past and future.
In a long-winded way, Diamond is arguing for history to develop itself, and be taken seriously, as a science. This, he states, will be of benefit to us because it will tell us how we got "here", and where we might be going.
Diamond specifically compares history to sciences such as astronomy, in which the scientist is limited to observational data and cannot conduct laboratory tests, or to the epidemiologist, who is prohibited from experimenting on humans in ways which would harm them or be otherwise morally objectionable. Diamond sees history not as a collection of facts, but as a series of simultaneously occurring experiments which can be analysed for broad patterns and outcomes dependent upon the variables.
Diamond also makes several (unsubstantiated) suggestions that practitioners and advocates of the "hard sciences", such as physics, "look down" on, or are "ignorantly disdainful" of those which are less empirical, such as his own fields. This is telling because many of Diamond's critics point specifically to his lack of experience in the fields he attempts to incorporate into his arguments, and the way his evidence conforms to his conclusions rather than the reverse, suggesting that Diamond is attempting to discredit his critics as "not real scientists", or at least as insufferable ideologues. This should especially be taken into consideration depending upon whether one views Diamond as an empirical anthropologist or as a book salesman.