So, if you aren't rooted, my comments above are a no-go.
However, you can accomplish the same thing by using chrome devtools' remote debugging.
Start by plugging your android device into your computer and firing up chrome. Then, in the chrome dev tools, click the hamburger button --> More tools --> Remote Devices.
As long as you've enabled USB Debugging on your android device, you should be able to select your phone from the list of devices. This displays all of the tabs you have open!
From there, you can select-all and copy to get your tab URLs.
Note: if a tab has a "long" URL, it will be shortened with an
… in the middle of the URL. If you specifically need URLs that have been shortened like this, be sure to right-click the link and copy the full URL!