puppeteer screen capture demo. Currently records 10 second video. Change the timeout in background.js with your own logic to stop the recording when necessary. Try with `node export.js`

background.js

/* global chrome, MediaRecorder, FileReader */

chrome.runtime.onConnect.addListener(port => {
  let recorder = null
  port.onMessage.addListener(msg => {
    console.log(msg);
    switch (msg.type) {
      case 'REC_STOP':
        console.log('Stopping recording')
        if (!port.recorderPlaying || !recorder) {
          console.log('Nothing to stop')
          return
        }
        port.recorderPlaying = false    
        recorder.stop()    
        break
      case 'REC_CLIENT_PLAY':
        if (port.recorderPlaying) {
          console.log('Ignoring second play, already playing')
          return
        }
        port.recorderPlaying = true
        const tab = port.sender.tab
        tab.url = msg.data.url
        chrome.desktopCapture.chooseDesktopMedia(['tab', 'audio'], streamId => {
          // Get the stream
          navigator.webkitGetUserMedia({
            audio: false,
            video: {
              mandatory: {
                chromeMediaSource: 'desktop',
                chromeMediaSourceId: streamId,
                minWidth: 1280,
                maxWidth: 1280,
                minHeight: 720,
                maxHeight: 720,
                minFrameRate: 60,
              }
            }
          }, stream => {
            var chunks=[];
            recorder = new MediaRecorder(stream, {
                videoBitsPerSecond: 2500000,
                ignoreMutedMedia: true,
                mimeType: 'video/webm'
            });
            recorder.ondataavailable = function (event) {
                if (event.data.size > 0) {
                    chunks.push(event.data);
                }
            };

            recorder.onstop = function () {
                var superBuffer = new Blob(chunks, {
                    type: 'video/webm'
                });

                var url = URL.createObjectURL(superBuffer);
                // var a = document.createElement('a');
                // document.body.appendChild(a);
                // a.style = 'display: none';
                // a.href = url;
                // a.download = 'test.webm';
                // a.click();

              chrome.downloads.download({
                url: url,
                //filename: "suggested/filename/with/relative.path" // Optional
              });
            }

            recorder.start();

            setTimeout(()=>{
                recorder.stop()
            }, 10000)
          }, error => console.log('Unable to get user media', error))
        })
        break
      default:
        console.log('Unrecognized message', msg)
    }
  })
})

content_script.js

window.onload = () => {
  if (window.recorderInjected) return
  Object.defineProperty(window, 'recorderInjected', { value: true, writable: false })

  // Setup message passing
  const port = chrome.runtime.connect(chrome.runtime.id)
  port.onMessage.addListener(msg => window.postMessage(msg, '*'))
  window.addEventListener('message', event => {
    // Relay client messages
    if (event.source === window && event.data.type && event.data.type.startsWith('REC_CLIENT_')) {
      port.postMessage(event.data)
    }
  })

  document.title = 'pickme'
  window.postMessage({ type: 'REC_CLIENT_PLAY', data: { url: window.location.origin } }, '*')
}

export.js

const puppeteer           = require('puppeteer');
console.log(__dirname)
var options = {
  headless: false,
  args: [
    '--enable-usermedia-screen-capturing',
    '--allow-http-screen-capture',
    '--no-sandbox',
    '--auto-select-desktop-capture-source=pickme',
    '--disable-setuid-sandbox',
    '--load-extension=' + __dirname,,
    '--disable-extensions-except=' + __dirname,
  ],
  executablePath: 'google-chrome-unstable',
}
puppeteer.launch(options).then(browser=>{
    return browser.pages().then(pages=>{
        var page = pages[0];
        return page.goto('http://tobiasahlin.com/spinkit/', {waitUntil: 'networkidle2'}).then(_=>{
            return page.evaluate(()=>{
                var session = {
                    audio: false,
                    video: {
                        mandatory: {
                            chromeMediaSource: 'screen',
                        },
                        optional: []
                    },
                };
            })
        })
    }).then(_=>{
        // return browser.close()
    })
})

manifest.json

{
  "name": "Video Capture Attempt #1",
  "version": "0.1.0",
  "manifest_version": 2,
  "background": {
    "scripts": ["background.js"]
  },
  "content_scripts": [{
    "matches": ["<all_urls>"],
    "js": ["content_script.js"],
    "run_at": "document_start"
  }],
  "permissions": [
    "desktopCapture",
    "<all_urls>",
    "downloads"
  ]
}