just to be clear, the link would go to the page/post on one's website where the video is embedded (not to youtube etc. site itself)

Directing the click to the particular Composr URL where it's hosted isn't viable without a lot of work, because whatever is processing the Comcode would not know the origin of the Comcode. This is particularly true for e-mails, which are written up as Comcode then just requested to be sent - the mailer asks the Comcode parser to parse the Comcode, but the mailer doesn't know where the Comcode came from. In the case of "What's new" newsletters this is even more problematic because that content is amalgamated from many sources.

How about if there's just no link on the thumbnail if you don't want one? I can make a quick hidden option to suppress putting in the link to YouTube. The "What's new" mails already contain a link to go back to view the content, so extra links on the thumbnails would be superfluous anyway.

Actually hold on that, I may be able to do a smart trick to make it configurable in templates.
One of 3 configurable behaviours:
1) No link
2) Link to original media URL (e.g. to YouTube)
3) Link back to content

I'm fine with your simple idea to not have any link on the thumbnail because as you say there is already a link back to the content.
It's important for users to go to our website to view the video, since it's part of an article.