I don’t know what plugin you are referring to, so maybe it does other things for you. But the above is not necessary to simply embed media.
As BLUEFROG says, you can use the file path of indexed files.
As meowky suggests, you can use proper HTML. This also allows you to specify attributes for the video. Or you can use standard markdown links or WikiLinks.
The following syntax is compatible in both Obsidian and DEVONthink:
![[movie.mp4]]

(document and video located in same folder)
<video src="../Assets/Video/movie.mp4"></video>
The last one actually surprised me. The manual states (p. 42, Linking): “it’s not possible to travel up with ..
as documents can have multiple parents” – but I guess that is only for internal files. For indexed files, a document should have only one parent.
At first ../
didn’t work for me in MD, and I thought it only worked in HTML. Then I realized I forgot to URL-encode a couple of spaces in the path, and it worked:

Obsidian also supports this syntax, which I had never seen before:

Apparently it is part of the CommonMark spec (documented here), but it is not supported in MultiMarkdown. So it doesn’t work in DEVONthink.
Personally I don’t get the appeal of embedding videos in your recipes. I would find it too cluttered. When I cook, I cook – I’m watching the food and don’t want to be watching a video. If I want to reference a video, I would just use a normal URI link. In that case x-devonthink-item
links work just fine.
Out of curiosity, what plugins do you use for recipes?
If you’re up for it, I guess you could also write some custom CSS for recipes in DEVONthink. I’ve toyed with the idea before… I would mainly want the ingredients listed in a separate column. But as I rarely wish for multi-colum layouts, I haven’t learned about them yet, so I can’t help you there.