Just joined this StackExchange to show some appreciation for [Jeremy's answer](https://android.stackexchange.com/a/177760/258950) above, and also add the few lines of JS I used to export the tabs list (since copying with the cursor isn't ideal!)

As Jeremy said, select `Remote devices` under `More tools` on Chrome devtools `⋮` icon (top right of the panel):

[![][1]][1]

- set up USB debugging on your phone (under `Settings`⇒`Developer options`, root not required)
  - note that you must enable the `Developer options` menu, it's hidden by default to protect users
  - on my phone this required tapping multiple times on the build number under `Settings`⇒`About Device`
- once this is done, plug your USB in and allow MTP connection
- when the Chrome devtools remote device panel is open, the phone will then request to allow USB debugging
  - you can opt to always trust the computer

[![][2]][2]

Now the device is connected,

- open a 2nd devtools view on the devtools view from which you selected `Remote devices` to be able to retrieve the list of tabs using JavaScript
  - note that you must have devtools in pop-out mode (use the vertical ellipsis symbol in the top right of the panel) to be able to get this up, otherwise `Ctrl`+`J` will just close the first devtools panel.
- expand the list from the first few items to all tabs by clicking 'Show more'
- to script against the list, use the following few lines of code [entered in the console of the 2nd devtools window]
  - N.B. `/deep/` is the CSS selector to enter `#shadow-root` DOM elements

[![][3]][3]

To export a list of all URLs open on Chrome for Android, I chose to just make the list into a markdown formatted text string and copy it to the clipboard

<!-- language: lang-js -->

    tabs = Array.from(document.querySelectorAll('div /deep/ div /deep/ div /deep/ div /deep/ div /deep/ .device-page-list .vbox'), s => ({name: s.querySelector('.device-page-title').textContent, url: s.querySelector('.device-page-url .devtools-link').href}))
    str = '';
    for (i=0;i<tabs.length;i++){
      str += '['+tabs[i]['name']+']('+tabs[i]['url']+')\n'
    }
    copy(str)

You will then have a list on your clipboard looking like this:

    [How can I export the list of open Chrome tabs? - Android Enthusiasts Stack Exchange](https://android.stackexchange.com/questions/56635/how-can-i-export-the-list-of-open-chrome-tabs)
    [Get Started with Remote Debugging Android Devices  |  Tools for Web Developers  |  Google Developers](https://developers.google.com/web/tools/chrome-devtools/remote-debugging/)
    [How To Enable USB Debugging On Your Android Phone](https://www.groovypost.com/howto/mobile/how-to-enable-usb-debugging-android-phone/)
    [Configure On-Device Developer Options | Android Studio](https://developer.android.com/studio/debug/dev-options.html)
    ...


  [1]: https://i.sstatic.net/aWqoo.png
  [2]: https://i.sstatic.net/I6rZs.png
  [3]: https://i.sstatic.net/0NERa.png

### Update

For some reason I'm getting an error _some of the time_, saying it failed to get the `href` attribute of a `null` item (when I inspect it it's an invisible node, who knows). To step around this, use this version instead:

<!-- language: lang-js -->

    tabs = document.querySelectorAll('div /deep/ div /deep/ div /deep/ div /deep/ div /deep/ .device-page-list .vbox')
    str = '';
    for (i=0;i<tabs.length;i++){
      if (tabs[i].querySelector('.device-page-url .devtools-link') != null){
        str += '- ['+tabs[i].querySelector('.device-page-title').textContent + '](' + tabs[i].querySelector('.device-page-url .devtools-link').href +')\n'
      } else {
        console.log(tabs[i])
      }
    }
    copy(str)