Essentially the term geopolitics refers to the "geographical settings and their relationship to political power .... spatial frameworks embracing political power units such as hemispheres, oceans, land and maritime boundaries, natural resources and culture."  (B Chapman, Geopolitics (Praeger Publishing, Santa Barbara, CA, 2011) 2).  Classical geopolitics as it emerged from early 20th century Germany considered that a state's geography defined opportunities and limitations in matters of political power.  The focus here is on military matters, national security, economic power, and state expansion.  Understandably, this approach became less popular after WWII.  Critical geopolitics takes a wider view.  While remaining focuses on the central influence of geographical/territorial boundaries of states or non-states, it expands its remit to include how geography influences international affairs, diplomacy, power relations and popular/cultural understandings of how that power is constructed and exercised (how does the territorial unit see itself - both from within and in relation to other entities).  Recent additions to the field include issues such as terrorism and climate matters.  

Academic writings on geopolitics definitely include small states/jurisdictions and/or islands as a sub-type of geopolitical interest.  Some examples are:

• P Claesson "Continental Hegemony and the Geopolitics of Island Basing: A Preliminary Approach to Ethnic Identification and Political Mobilization in Militarized Island Communities" (2008) Scandia 87 - discusses the importance of islands for continental powers.  Sark clearly fits within this paradigm and its history reflects this. 
• BMW Ratter "Geopolitics of Small Islands" in BMW Ratter Geographies of Islands (Springer, Cham, Switzerland,  2018). Similar to above - considers "islands as pawns in the game of international interests and territorial powers. It deals with the spatial location of islands and the associated geopolitics."
• Jeane A.K. Hey, “Introducing Small State Foreign Policy,” in Jeane A.K. Hey (ed.) Small States in World Politics: Explaining Foreign Policy Behaviour, (Lynne Rienner Publishers, Boulder, 2003)
• Laurent Goetschel (ed .) Small States Inside and Outside the European Union: Interests and Policies. (Kluwer, Boston, 1998)