The best way is to do it via HTML and CSS like robin mentioned in his comment. If you wanna do the same in Markdown, or just without using CSS, read on...

I made an open-source API to add a play button to Youtube thumbnails given a Youtube id or URL, simply input the video URL to this API i developed like so: https://markdown-videos-api.jorgenkh.no/url?https://youtu.be/dQw4w9WgXcQ

Result:

Documentation can be found here if you wanna customize the size: https://markdown-videos-api.jorgenkh.no/docs

I even made a website to make it easier for you to input video URLs: https://markdown-videos.jorgenkh.no/

And best of all, the code is fully open sourced, so you can fork it and host it yourself if you'd like: https://github.com/Snailedlt/Markdown-Videos