What does "the height of inhumanity" mean in the context?

The height of inhumanity means the in the most inhumane manner or the most extremely cruel, brutal behavior, (a crime against humanity)

Sun Tzu's argument is: war always brings frightful misery and vast expenditure of blood and treasure. A war may drag on for years unless you are kept informed of the enemy's condition, and are ready to strike at the right moment. The only way to get this information is to employ spies, and it is impossible to obtain trustworthy spies unless they are properly paid for their services. But it is surely false economy to grudge a comparatively trifling amount for this purpose, when every day that the war lasts eats up an incalculably greater sum. This grievous burden falls on the shoulders of the poor, (referred to earlier as "men lacking at the plough-tail") and hence Sun Tzu concludes that to neglect the use of spies is nothing less than a crime against humanity.

Sun-Tzu (who did not write in English) is speaking of spending money to save lives in your army; it being inhumane to allow your troops to die if you could simply bribe a few enemy soldiers to tell you of their positions, movements and/or routine.

Ditto Susan and Janus, let me just add a possible clarification: "the height of" is a common idiom meaning the extreme case of something. It can be positive or negative. "He displayed the height of ignorance when he made that absurd remark." "Sally always demonstrates the height of fashion and style." Etc.