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.
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.