Why did IS make their executions public?

IS publicly and gruesomely executed two American journalists. In the videos that showed this, they threatened Obama and America.

This seems crazy to me.

By doing this they basically paved the way for Obama to do anything he wants as far as attacking IS.

So, IS is either very out of touch with American politics, or the group that posted the video is not IS, and wants America to advance their efforts against IS.

Can someone help me out here?