It's actually how VSCode started :). It was supposed to be web based IDE, then Atom and Electron happened and Monaco was put into Electron shell and that became VSCode.
Really!? Source on this?
Yes, and Monaco is alive in VSTS(Team Services) and Azure's web app IDE. :)
Well, VSO(VS Online) was used internally by MS way before VSCode was an idea.
It's the text editor control (used, e.g., in Visual Studio Team Services). The editor (incl. plugin system, IO, ...) is afaik not available as a webpage.
It's a little bit more than only an editor. E.g. it contains the complete framework for custom languages with syntax highlighting, auto completion, annotations, etc. You can easily plug in support for your custom languages there.
What it doesn't contain compared to VsCode is multiple panes, file management, etc.
You can of course build file management on top of the base Monaco component. Monaco itself provides only APIs to set or retrieve the content of a monaco editor widget. You can then build some kind of filemanager on top of it which loads file contents from whereever and puts them into an editor instance.