I don't see Node.js and Homebrew as "web related".
Tell me again how Node.js is not web related?
(Homebrew is, quite as you say, not web related.)
Nothing web-related in this project, for example: https://github.com/neandrake/spirc
... except a several million line JIT
Even if there are, I still feel that Javascript is too completely dependent on its position in web browsers for Node.js to be entirely disassociated with the web. If a new language would replace Javascript in the browser, Node.js would be instantly abandoned. But I could see your point.
Or npm (https://github.com/npm/npm), a package manager?
Npm uses Web protocols (HTTP, maybe JSON-RPC) to communicate with repository servers.
This is not saying that there aren't any non-web applications using Node.js, just that web-related applications using Node.js are quite numerous and popular.
Personally I know of Node.js applications and libraries targeting robotics, computer vision, language analysis, neural networks and more. Like any powerful platform, much of this relies on the ability of Node.js to interface with external libraries, which it does using wrappers built with node-gyp.
Node became my vanilla language nowadays. Countless are the CLI utilities that I made/use that are written with it (I practically don't write shell scripts anymore).
And of course, don't forget that networking is broader than internet which is broader than web. I'm solely talking about web here.