They do not. You can, however, add annotations in the form of arrows, circles, boxes or text to show your audience where to look.

The attached video shows you an example.

NEW BEHAVIOR after update to Version 2.3

Now, you can include your ROIs, and many other annotations, in the exported MP4 video. When you click the "Export Video" icon, you will be presented with the screen shown below. Click the "Include Data Plots" check box and then select the items you want to include in the video.