[…] and His Imperial Majesty further agrees to pay to the British Government the sum of Three Millions of dollars, on account of debts due to British subjects by some of the said Hong merchants (or Cohong), who have become insolvent, and who owe very large sums of money to subjects of Her Britannic Majesty.
(idiomatic) For the sake of.
When the object of this preposition is brief and animate, the alternative construction on someone's account is often used instead. If the object is a personal pronoun, that construction is more common; for example, on my account is more common than on account of me.
Similarly, on that account, using that as a determiner, is more common than on account of that.