The の is in fact が here. Take the sentence and cut that little phrase to make it easier to see:
人間対応能力は、「他の人間とともに働く能力」のことです。The ability to get along with people is "the ability to work together with other people."
Now the author just attributes the quote to Drucker with the short modifying phrase ドラッカーのいう. This could be ドラッカーがいう, but の is used in cases where the modifier is kind of subordinate; it marks the subject of the modifying phrase but not of the entire sentence, I guess.
So basically it works out to: The ability to get along with people is what Drucker calls "the ability to work together with other people."
Other examples of the の replacing a が:
犬の舐めたボールを触るな！ Don't touch balls that dogs have licked! (Ok, that example sounds dirtier and more awkward than I intended it.)
田中さんの選択した曲がかかってきた時、すごい盛り上がってきた。 When the song that Tanaka-san selected came on, he got super excited.
I guess a similar situation in English is choosing between that and which in modifying phrases.