A&R's story has two dimensions: economic and political institutions. The economic institutions story is basically Adam Smith’s: “peace, easy taxes and a tolerable administration of justice” lead to economic growth. For most of the past two centuries, with some unfortunate exceptions, this has been the conventional wisdom. The question is how you get good economic institutions. Here they argue that good political institutions, which allow people to control their rulers, are important. This is the nub.
A&R don’t list any particular institutions as always inclusive. Is democracy inclusive? (This blog post of theirs offers some relevant thoughts.) It certainly allows people to control their rulers and a change to democracy is likely to generate large one-off gains as policies are altered to benefit the people, not the elite. However, the potential for extraction (transfer of money from the many to the few) persists, for two reasons.
First, many political systems have very limited competition. For example, first past the post systems are basically duopolies, because once two parties are ahead in the polls, it makes no sense to vote for a third party. On subjects where competing parties share interests they will soon agree not to offer the voters a choice.
Second, voters are rationally ignorant of policy, and therefore easily swayed by intellectual fads and media manipulation. (I think A&R's blog post claim, "[t]he available evidence doesn’t indicate that the uneducated masses are ignorant and irrational" is quite wrong, if by "uneducated masses" you mean voters, and by "ignorant and irrational" you mean ignorant and rational. There is a ton of evidence for rational ignorance.) This allows for a lot of extraction behind their backs.
Another dimension is long-run prudence. A monarch who will tax his people ruthlessly may also take care of their long-term well-being, because he will benefit from it. A democratic ruler may provide short-run benefits to people for fear of losing office. But because he may lose office, and expects only to be in power half the time or less in future, he may also have few incentives to do the right thing in the long run. This means that democracies may under-insure themselves against rare risks, and may accumulate long-term weaknesses and vulnerabilities.