Implement chrome.fileSystem.requestFileSystem().

ui/file_manager/video_player/manifest.json

 {
   // chrome-extension://jcgeabjmjgoblfofpppfkcoakmfobdko/
   "key": "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAw0/gRbJc545iEGRZs20Rl/HtrSUp8H3gJd4Y6hCe0CG1xQiJhZ5nc8qZyxa96gMxRAKBq54S6sjVVtV6uS70oU6FvrvwItByYkkqr4ZE7eMJKwMqnGItxWbh6KBodf89lpKoIy6MtYTqubBhXB/IQBZsXah90tXwRzaaJNWw+2BBRIhcPsH3ng+wgN7rwFxo4HIv9ZpqkYlx90rwkfjOmKPPnSXyXFIBJfmqfdbd8PLtcxzzOTE+vxwoXZuYWrthKm4uKfNqXIYns74sSJlqyKfctuR+nQdNh8uePv0e+/Ul3wER1/jIXULLjfyoaklyDs+ak3SDf+xWScJ+0LJ0AwIDAQAB",
   "manifest_version": 2,
   "name": "Video Player",
   "version": "1.0",
   "description": "Video Player",
   "display_in_launcher": false,
   "incognito" : "split",
   "icons": {
     "16": "images/icon/video-player-favicon-16.png",
     "32": "images/icon/video-player-32.png",
     "48": "images/icon/video-player-48.png",
     "64": "images/icon/video-player-64.png",
     "96": "images/icon/video-player-96.png",
     "128": "images/icon/video-player-128.png",
     "256": "images/icon/video-player-256.png"
   },
   "permissions": [
     "commandLinePrivate",
     "fileSystem",
     "fileBrowserHandler",
     "fileManagerPrivate",
+    {
+      "fileSystem": ["requestFileSystem", "write"]
+    },
     "fullscreen",
     "mediaPlayerPrivate",
     "metricsPrivate",
     "power",
     "storage",
     "chrome://resources/",
     "chrome://theme/"
   ],
   "file_handlers": {
     "video": {
@@ skipping 48 matching lines @@
     },
     // The following ids are cast extension's ids .
     // - boadgeojelhgndaghljhdicfkmllpafd (release)
     // - dliochdbjfkdbacpmhlcpmleaejidimm (beta)
     // - hfaagokkkhdbgiakmmlclaapfelnkoah
     // - fmfcbgogabcbclcofgocippekhfcmgfj
     // - enhhojjnijigcajfphajepfemndkmdlo
     "content_security_policy": "default-src 'none'; script-src 'self' chrome://resources chrome-extension://boadgeojelhgndaghljhdicfkmllpafd chrome-extension://dliochdbjfkdbacpmhlcpmleaejidimm chrome-extension://hhaomjibdihmijegdhdafkllkbggdgoj chrome-extension://fmfcbgogabcbclcofgocippekhfcmgfj chrome-extension://enhhojjnijigcajfphajepfemndkmdlo; style-src 'self' chrome://resources 'unsafe-inline'; img-src 'self' chrome://theme chrome://resources data: https://www.googledrive.com; media-src 'self'; object-src 'self'"
   }
 }