My mistake -- it looks like when loaded as a file:// URL the remote runtime won't load.
You can add:
<script src="https://cdn.jsdelivr.net/gh/tumult/hype-runtime@728/HYPE-728.thin.min.js" integrity="sha256-Ed1c3/RZpROHZwlvrdp4NPjUocPlRvpZmeWtOEMq7co=" crossorigin="anonymous"></script>
...to the head of your exported .html document (by editing the 'head' in Hype). This is fine to leave in place for production but would need to be updated after a Hype update.
I got this embed code from the CDN's page: https://www.jsdelivr.com/package/gh/tumult/hype-runtime by clicking on 'Copy Html + SRI' for the build number:
(Note that there are features which may require the 'full' runtime listed here: Hype javascript size: When full.min.js is used instead of thin.min.js )