Except for most people that isn't the case. Most people are monogamous, therefore the relationship is assumed to be monogamous until discussed and agreed otherwise.
I think it's always a good idea to talk about the bounds of a relationship - unexpressed assumptions cause problems in relationships. I think mono people can learn some things from poly sorts
And, no, the best assumption is that you are dating until you agree on exclusivity. And once you agree to be exclusive it's good idea to share your assumptions of what the relationship will look like.
It is established that the player and SH are exclusive at the end of act 2. Plus most people will assume she means she wants to be with you now and always, as meaning only you. You may look at things differently, but the vast majority would take this as meaning monogamy.
