I think the license attached to the game would permit this (GPLv3), but anything derived from it would need to be released under the same license, including the source code.
Internally a Twine based story/game HTML file consist of a number of different parts, some of them being:
1. The
Textual content written by the story/game Author.
2. The
Programming Logic content written by the story/game Author.
3. Each of the third party JavaScript libraries that the story/game Author embedded in their project content.
4. Each of the Image & Audio assets the story/game Author included with their released builds.
5. The code specifically written by the Developer of the Story Format (eg. SugarCube, Harlowe, etc...) template file, into which the Author's meta Passage is embedded.
6. Each of the third party JavaScript libraries that the Story Format Developer included in the Story template file they created.
...and each of those parts can be Explicitly and/or Implicitly covered by their own copyright related licence.
"Twine" itself does not require an Author to use any specific licence, nor that the generated HTML file that the Author releases be licenced as "open source", that is totally left up to the Author's discretion.
So take care when assuming that the entirety of the generated HTML file is covered by the GPLv3 licence (or any other open source licence), when it may only be specific parts of that file.