How to capture image of Youtube Video and display on web site

Question

You can use YouTube IFrame API (see https://developers.google.com/youtube/iframe_api_reference).

Here is an example for playing the video provided in your question (gbcmYbMB9mo):

<body onload="LoadYouTubeIframeAPI()">
    <script type="text/javascript">
        var player = null;
        var playerParams =
        {
            playerVars:
            {
                "enablejsapi":1,
                "origin":document.domain,
                "rel":0
            },
            events:
            {
                "onReady":onPlayerReady,
                "onError":onPlayerError,
                "onStateChange":onPlayerStateChange
            }
        };
        function LoadYouTubeIframeAPI()
        {
            var scriptElement = document.createElement("script");
            scriptElement.src = "http://www.youtube.com/iframe_api";
            var firstScriptElement = document.getElementsByTagName("script")[0];
            firstScriptElement.parentNode.insertBefore(scriptElement,firstScriptElement);
        }
        function onYouTubeIframeAPIReady()
        {
            player = new YT.Player("player",playerParams);
        }
        function onPlayerReady(event)
        {
            player.loadVideoById("gbcmYbMB9mo");
        }
        function onPlayerError(event)
        {
            ...
        }
        function onPlayerStateChange(event)
        {
            if (event.data == YT.PlayerState.ENDED)
            {
                ...
            }
        }
    </script>
</body>

You might need to "play a little" with this code in order to prevent the video from starting automatically...