I had tried compiling directly to HTML, but, as you say, it creates a complete web page with HTML head and body container.
That’s a somewhat hidden MultiMarkdown quirk in how it works, in that if you supply an .md file with document-oriented metadata at the top of the file, then it will presume you want a document. If you do not then you will get a snippet that is meant to be pasted into boilerplate. So by default Scrivener inserts Title and Author metadata fields—as naturally most people do want a full document when they compile. If you delete both of those fields from the compiler, you will get a snippet.
If you don’t want to remove that metadata for whatever reason, then add the --snippet command-line flag to the Processor pane setup.
Here is some example content compiled from Scrivener, using the --nolabels flag and metadata removed, from to top to bottom of the file.
Clean output...
<h1>Red Book</h1>
<h2>scene a</h2>
<p>Some content…</p>
<h2>scene b</h2>
<p>Some more content…</p>
<h1>Black Book</h1>
<h2>scene c</h2>
And here is a sample compile Format.
clean-compile.zip (8.3 KB)
Update: edited .zip to include both a Mac and Windows variant, each using the default Scrivener install location for locating the multimarkdown executable embedded within it.