The meaning of example in this case is "a pattern or model; something to be imitated or avoided." Another example of when this would be used is the phrase, 'lead by example', which means to set a model/pattern that is meant to be imitated. That sentence alone most likely is meant to read, "Management is (done) largely by example.", which means that the ones 'managing' are constantly setting an example for those below them to follow. It can also mean that they are managing by following a set pattern.

"To set an example" means you do something to show how other people should do it. So, "management is largely by example" means the managers mostly demonstrate instead of instruct.