Right click anywhere on the table for a menu that will allow you to turn on or off Player or Observer Chat. If the Player chat box is checked and the Observer Chat box is not checked, then you will see only Chat from Players at your table.

At the top of the chat screen is a drop down menu. When you click on the drop down box, you can filter chat using any of the options listed there by clicking on them, such as: Quiet, Chat, Results & Chat, Results Only, Play & Chat, Play Only, or Everything.