По­яс­не­ние. Кон­текст тре­бу­ет ис­поль­зо­ва­ния су­ще­стви­тель­но­го: ...with China dropping to second place on the medals table after unprecedented dominance at their home Olympics in Beijing four years ago.  =  ...а Китай опу­стил­ся на вто­рое место в таб­ли­це ме­да­лей после бес­пре­це­дент­но­го до­ми­ни­ро­ва­ния на своей до­маш­ней Олим­пиа­де в Пе­ки­не че­ты­ре года назад.

Dominance: the quality of being more important, successful or stronger than anything else of the same type (The party's dominance in Scotland was being challenged for the first time / The dominance of the car makes cycling and walking increasingly difficult / The company's growing dominance of the sports shoe industry).

Domination: power or control over other people or things (The movie was about a group of robots set on world domination (=  control of all countries) or the state of having control over people or a situation (Her domination of the tennis world is undisputed).

Ответ: dominance.