Specific support for ExtJS controls appeared in TestComplete 9.20. All previous versions of TestComplete will "see" these controls like plain HTML web page.
Load your application in Chrome, open Object Browser in TestComplete and in one of the Process("chrome") nodes you should see child Page object corresponding to your web page. Do you see this Page object? Does it have children representing objects in that page?
What is in the recorded script? Do you have the same problem with any web page (try recording a couple of actions on smartbear.com)?