how remove "open new tab" button ? The embedded link directly from Google Drive doesn't seem to allow you to remove the button that opens the video in a separate tab nor customize the appearance of the player.
Replace "videoID" in the link with your video ID. (to find it - right click on the Google Drive video, get shareable link)
<video>
<source src="https://drive.google.com/uc?export=download&id=videoID" type='video/mp4'>
othersolution