Unless you are trying to implement a Player card, you do not need to be whitelisted or approved. The error message is misleading, and almost certainly means that the validation tool cannot see any twitter:card markup in your page.
Can you check that when you view source of your page, the expected Twitter Cards meta tags are shown? if not, you may need to check your plugin configuration. Note that we provide our own official Wordpress plugin, but cannot easily provide support for those built by third parties.
Otherwise, if you are able to share a link, someone may be able to take a look.
