Check it twice, what the submission implements is writing all the UI in markdown, not mixing markdown with React.
Perhaps I don't know mdxjs enough but that's my impression.
MDX goes a step further by enabling you to actually write the component JSX in the Markdown as if it's React (rather than using ``` syntax). You can just display a component that was loaded from somewhere else. Basically, if you took the Markdown UI components as React components, you could use the runtime embed option from here: https://mdxjs.com/guides/embed/
MDX parses JSX so it's compatible with any JSX runtime, not just react.
You're right that MDX executes arbitrary code because it supports the `import` and string interpolation of MDX and performs unsafe evals.
Because those evals aren't safe to use at runtime, I actually created a library that uses the MDX parser to support the static subset of JSX (which is very similar to HTML making it static and secure): https://www.npmjs.com/package/react-markdown-with-mdx