It’s worth noting that there is a pretty specific theme:

Humans live on a finite planet on which we depend to survive. Earth operates as an integrated, intricate, and fragile ecosystem, containing myriad layers of interdependency between nature’s systems and living beings – both human and non-human. These systems are geochemical, biological, social, and computational. For the first time in human history, a rapidly developing, planetary-scale technostructure of sensors and supercomputers is enabling us to perceive, monitor, and predict this vast and complex system. In so doing, technology is making the world seem smaller, and our collective belonging to it and each other more undeniable.
In short, the planetary technostructure that humans have created and in which we are embedded is revealing our condition of planetarity — that is, the inescapability of our embeddedness in an Earth-spanning biogeochemical system in which humans cannot thrive unless the ecosystems we inhabit are themselves thriving.
This emergent condition demands a novel framework to parse philosophical, institutional, and political realms.
To date, most ideas about our shared future on this scale have centered on the global (an extension of the traditional nation-state), the international (politics, economics and infrastructures of the global), and the human (other than and dominant over nature). The nation-state is a type of sociopolitical architecture that has historically tended to foster self-interest and encourage competition. The planetary, which represents conditions and ways of being that exceed the human and our anthropocentric categories, is an opportunity to recast both the players and the play.
The Berggruen Institute proposes further developing the concept of the planetary. Framed as an invitation to a deepening understanding of the planet and our shared fate with all living beings, as well as our emerging ability to shape it, it invites us to reevaluate our relationships to each other, to nonhuman others and to the planetary whole. We are looking for new frameworks and categories to understand life on Earth, new ideas that decentralize the human as the premise for understanding the world and building institutions that effectively manage it.
Here are some examples of topics that could be tackled:

• Philosophical conceptions of the self in a planetary context;
• New or adapted models of governance that would be optimized for planetary thriving;
• The definitional instability of the category of "life" as it relates to the planetary;
• The limits of the sovereign liberal subject codified by Western philosophy to understand planetary interconnectedness and embeddedness;
• The concept of planetary citizenship as it relates to issues of inclusion and agency;
• Novel theories of technology in the age of AI, social media and computation that disclose the condition of planetarity;
• Models of governance optimized for multispecies flourishing and whole-planet thriving;
• The extraplanetary: Earth as a particular planet that has evolved life of one of many planets that might or might not host life;
• Ideas from non-Western philosophy that inform the planetary;
• Simulations, virtual environments and AIs that transform traditional perceptions of the planetary;
• Nomos of the cloud: New political geographies in a digital world.

We invite you to conceive of and select your own topic related to the planetary as well.

I was intrigued until I saw that they want references and to know where you studied, etc.

Mind you I haven’t participated in many essay competitions, but I’ve never seen one that requires character references!

This is also worth noting:

"By entering this competition, the entrant grants the Berggruen Institute a non-exclusive, royalty-free, fully paid, perpetual, irrevocable, and worldwide license to reproduce, distribute, display, and create derivative works of the submitted essay (along with a name credit) in connection with the competition and promotion of the competition, in any media now or hereafter known. To that end, when you upload, share with, or submit an essay to us, you grant us the non-exclusive, royalty-free, fully paid, perpetual, irrevocable, and worldwide license to: (i) use, host, store, reproduce, modify, prepare derivative works (such as translations, adaptations, summaries, or other changes), communicate, publish, publicly perform, publicly display, and distribute your essay in any manner, mode of delivery, or media now known or developed in the future; and (ii) permit other users to access, reproduce, distribute, publicly display, prepare derivative works of, and publicly perform your content through us (e.g., for users to re-blog, re-post, or download your content)."

I just read "The Tyranny of Time," one of the "exemplary essays that epitomize the genre and style that we look for." The following analogy will give you the gist. Suppose that I began an essay by pointing out all the ways in which the modern Western equal-tempered musical scale differs from natural scales. Then I strongly suggest that unnatural scales are in some important sense not real. Then I explain the existence of modern scales as driven by and fundamental to capitalism and European imperialism, blinding us to underlying reality and binding us with stultifying uniformity. I end with a general plea to return to nature.

(If anyone writes this essay, and wins, I expect a share of the proceeds.)