It's a nice big bonus, but it's not required per sé. Unless the game revolves around physics, that is. Can't have a physics based game without physics, right? =P
Games like Toribash use physics as a core part of the gameplay, while others, such as many first person shooters, use it for effects. These effects aren't necessary, but make the games so much more fun to look at. For example, if you blast someone in the chest with a shotgun, seeing them get sent flying in a physicsy way is loads more entertaining than a purely scripted death. The latter can look good if it's contextual (pistols causing slow crumbling, bazookas sending people barrelling through the air in gory pieces), but the former typically looks better if done right.
Long story short, not necessary, but a very big bonus if done right.