A game is usually a competitive activity between two competing sides. It's a dangerous game because it's involving the attempt of a murder of Rainsford by Zaroff via hunting. It's also dangerous because of the environment in which they dwell and the other forces working towards his downfall such as Ivan and the dogs. While games are usually fun and enjoyable, the title of The Most Dangerous Game is ironic in that it's a life or death situation and a battle of wits, and it involves being chased or found like in tag or hide and seek.
Ann is the subject of the sentence has taught is the verb phrase students is the direct object junior high are adjectives that modify the direct object students for several years is a prepositional phrase that modifies the verb taught