Yes, this quotation you attributed to Philippine President Rodrigo Duterte is a figure of speech known as chiasmus: “It is not the eagle in the fight but the fight of the eagle that matters.” Its fundamental structure and mechanism reverses the order of words in two parallel phrases. When done with finesse, such parallel word reversals—by some linguistic alchemy—can arouse our senses, disarming us so we readily accept their claim as true. Chiasmus has this power because it heightens the sense of drama in language by surprise. It is no wonder that it holds the distinction of being mankind’s all-time vehicle for expressing great truths and, conversely, also great untruths.
(http://josecarilloforum.com/imgs/chiasmus5_composite-1A6.png)
I have written in detail about chiasmus in “A figure of speech that’s often used to subvert reason and logic,” (http://josecarilloforum.com/forum/index.php?topic=5835.0) an essay that was posted in the Forum way back on May 4, 2013. Simply click the link to know more about it.