Here is a method for embedding video stored in your Google Drive. I've tested it with 2.7 but I don't see why it wouldn't work with earlier versions.
Upload your video to Google Drive
Right-click the video and choose "Share...”
Make sure sharing is set to "Anyone who has the link can view”
Copy the "Link to share” from the box at the top of the dialog
Paste and open the link in a new tab or browser
At the top of the screen, click the icon with three vertical dots and choose "Embed item...”
Copy the embed code
In Moodle, open (or create) the activity/resource where you want to place your video
In the editor (TinyMCE or Atto), open the HTML editor (<> in Atto)
Paste the embed code where you want your video to appear.
You may want to change the size of the video - Google's default is 640x480, which is a lot of screen real estate on most devices. Your users will be able to make it full screen if they wish.
Example HTML (The bold text is the embed code copied in step 8):
<p>My Video</p> <iframe src="https://docs.google.com/file/d/0Bw9mCKrvk_W3MXFKdTvxN7ZLdVE/preview" height="480" width="640"></iframe>