> Utilitarianism doesn't say that 'good is the sum total of happiness across all humans' but rather it says it's 'the greatest good for the greatest number', which is substantially different, so this is a distortion of the facts. I would refer the author to the works of Jeremy Bentham and John Stuart Mill especially his work Utilitarianism.
That's why the author mentions "specifically the version" of utilitarianism which does sum happiness across people (it's called Total Utilitarianism, by contrast with Average Utilitarianism). "The greatest good for the greatest number" is ambiguous, later thinkers have parsed it out in different ways.
Put two philosophers in a room and have them discuss utilitarianism and you'll end up with twenty opinions. Average utilitarianism is just one of its later fallouts. (I needn't tell you how unpopular utilitarianism is with many philosophers and others—especially in this era).
Fact is, the author used the splinter view to further his argument which hasn't worked. Given other weaknesses he would have been better to ignore utilitarianism altogether.
That's why the author mentions "specifically the version" of utilitarianism which does sum happiness across people (it's called Total Utilitarianism, by contrast with Average Utilitarianism). "The greatest good for the greatest number" is ambiguous, later thinkers have parsed it out in different ways.