Yes. It works on the main page, but not on the domain where your image is hosted.
<meta name="twitter:image" content="http://cdnweb01.wikitree.co.kr/webdata/editor/201612/19/img_20161219203728_8254828d.jpg">
The file http://cdnweb01.wikitree.co.kr/robots.txt contains:
User-agent: *
Disallow:/
Disallow:/main/ads/
Allow:/main/news_view.php
Allow:/webdata/editor
This blocks all user-agents (*) from accessing your image. You should review Google’s robots.txt spec. You can add an exemption for Twitterbot if you like.