Embed .mov file via ‘Add Media’ not working

You can try the following:

/**
 * Add support for the QuickTime (.mov) video format.
 */
add_filter( 'wp_video_extensions', 
    function( $exts ) {
        $exts[] = 'mov';
        return $exts;
    }
);

to add the Embed Media Player support for the QuickTime video files.

The default supported video formats are:

mp4, m4v, webm, ogv, wmv, flv

Update:

When I test this I get the Embed Media Player option and following shortcode inserted into the post:

Similar for the .avi and .wmv extensions: