I eventually figured out an easy way to do it:
- On your Twitter feed, click the date/time of the tweet containing the video. That will open the single tweet view
- Look for the down-pointing arrow at the top-right corner of the tweet, click it to open drop-down menue
- Select the "Embed Video" option and copy the HTML embed code and Paste it to Notepad
- Find the last "t.co" shortened URL inside the HTML code (should be something like this:
https://``t.co/tQM43ftXyM
). Copy this URL and paste it in a new browser tab.
- The browser will expand the shortened URL to something which looks like this:
https://twitter.com/UserName/status/828267001496784896/video/1
This is the link to the Twitter Card containing the native video. Pasting this link in a new tweet or DM will include the native video in it!