Your content script must communicate with the plugin in page context.
That is, you need to put the code into a 'script' element:

  document.body.appendChild(document.createElement('script')).text = '(' + (() => {
    addEventListener('message', function _(e) {
      if (e.data && e.data.type === 'getSelectedTextReply') {
        removeEventListener('message', _);
        alert('SUCCESS:\n' + e.data.selectedText);
      }
    });
    document.getElementById('plugin').postMessage({type: 'getSelectedText'}, '*');
  }) + ')()';

To transfer the data back into content script you can use DOM CustomEvent.
Similar example: https://stackoverflow.com/a/46870005

@vaidas: Thanks for filing the issue! Could you please try once with comment #1 and if possible,Please create new profile without extensions and apps.Re-check once in latest chrome stable/canary and let us know the observations and sample steps of the issue which would help us to triage the issue further.

Thanks in Advance.

Comment #1 was a correct solution, selected text indeed get shown in the alert box. However, I have to criticize that we had to spend a whole week studying and rewriting the solution into more readable on the stackoverflow in the folowing link: https://stackoverflow.com/questions/49670116/why-unexpected-string-help-rewriting-ugly-code.

However, I still haven't transfered selected content to the content-script.
Due - I being really new to extension development.

I have tested the code snippet mentioned in comment #1 with a completely new profile, without any apps or extensions enabled.

It was tested in the stable Chrome Version 65.0.3325.181 (Official Build) (64-bit)

Marking it as WontFix as per comment#4 provided by user.Feel free to raise a new issue if still facing.

Thank You!