Sorry you’re having some trouble. Just to state up front, this is the ZBrush help forum, I’ve never used ZBrush Core, and if ZB Core functions in a different way in this regard, I wouldn’t know. This answer is based on the full ZBrush program.
Close ZBrush entirely, restart it, and in a fresh session load the DemoSoldier.ztl from the Lightbox> Tool directory (accessible via Tool> Lightbox > Tools, or by pressing the [ , ] key and navigating to it.
Attempt to export all the visible tools via the OBJ extended format the same way you have been. If it works successfully without issue, then the tool you were previously trying to export is problematic in some way. Without a lot more information, I would have no way of even guessing the reason for this. Remember, however, that ZB Core has a max polygon per Subtool limit of 20 million polygons, and cannot perform an operation that would result in a subtool with more polygons than this.
If you get the same errors, then there is an issue with your installation, and you should contact Pixologic Support. Technical issues, crashes and error messages should always be referred to support. The other users on the community forums aren’t equipped to troubleshoot system specific technical issues with your program.