When you share a player to Twitter, you should be able to see an inline player on the feed (desktop version). This is because Twitter can read the Twitter card tags that appear on your sharing page.
When you share your player, you see the full URL in the tweet, but no inline player.
You have likely used a CNAME for your sharing page that has not been whitelisted by Twitter. This means that the inline video will not display.
Use the Twitter Validator tool to confirm there is a whitelist issue when you enter your sharing page URL. If this is the case, there is an option to request a whitelist for your domain.
Note: if Twitter continues to not display the Vidyard player inline, you may also need to Enable search engine indexing on your sharing page. This exposes your sharing page to search engine crawlers like Google and allows Twitter to fetch the player metadata.
In this circumstance, an error like the following may appear on the Twitter Card Validator: