What the use case for something like this? Am I missing something?
If you can use the same code for both client and server, then it opens up the possibility of sending chunks of logic over the wire.
Here's a trivial example: a website uses Markdown for comment formatting. You can improve the feedback cycle, especially for those who aren't overly familiar with Markdown, by rendering a preview on the client side. However, this means that you need two Markdown parsers, one in your server-side language, and one in JavaScript. That's a potential duplication of effort. Someone has already written a JS Markdown parser, but it might not have exactly the same behaviour as your server implementation. So why not just write the code once and have it work on both sides?
I have a feeling that there are a lot more interesting things that you can do with split computation, but I haven't seen many examples yet. I think they'll come.