For editing in the browser, where you're likely to keep one tab open for a long time, it is an absolutely obvious choice. A huge undertaking for sure, and it's awesome that he was able to accomplish it!
The SourceGraph folks seemed to have been one of the first to get major chunks of VSCode running in browser. I've stumbled across a few others doing similar things but they seemed like toys.
What the creator is saying is that he got the actual VSCode project running in the browser. This means that the vast plugin ecosystem will run inside the browser. I suppose he'd have replaced all the nodejs dependencies with browser versions; for example an "fs" module that keeps files in-memory (or maybe using indexeddb) etc.
Further down that tweet, he says that the code is very easy to get started with. That's been my experience looking at it briefly; VSCode just seems like it was written by a team with deep expertise in IDE-making and PLs.
I used to be a major contributor and follower of Atom. People commonly asked why Atom couldn't run in the browser. The answer was simple, node and a browser are totally different things. Imagine a browser opening files, starting processes, running arbitrary C-code, etc.
No, VSCode does not normally run in a browser.