not able to open any of the Thingworx's widget file in Eclipse. Error: TW is undefined.

This is a basic Eclipse configuration issue. It's just that in Eclipse you do not have an editor for Javascript files setup. The current association for JS files in Eclipse is picked up from Windows - and apparently it's setup to Internet Explorer based on the error message.

The Window that pops-up in the background tells you exactly what needs to be done.