how does the phrase "of soccer" function in the sentence "the game of soccer has been played all over the world for centuries, but the game as we know it today was first played in the mid-1800s in England"

The phrase "of soccer" is used to specify the game that is being referred to in the sentence. It is functioning as an object of the preposition "of", which is used to indicate possession or association. Therefore, the sentence is referring to the game that is commonly known as "soccer" and the phrase is clarifying that it is this specific game that has been played all over the world for centuries.