Context: LaTeX is a typesetting system. When compiling a document, a lot of really in-depth debugging information is printed, which can be borderline incomprehensible to anyone but LaTeX experts. It can also be a visual hindrance when looking for important information like errors.
Hint: :q!
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This is what I though as well when I first looked at their website. But nope, the compiler and LSP are available as fully offline programs under the apache license. But I understand how you'd get confused, their website is strikingly polished for an open-source non-commercial project!
The only thing you're missing out on if you use the offline version is having the rendered preview update in real time as you type, but you can sort of emulate that feature using their neovim plugin and a really fast PDF viewer like zathura.
The last point: I use MuPDF + entr as zarhura crush as a mf, not usable at all. Some others use typst-preview which can be used in the browser and as a VS Code extension. But I use Neovim btw and the web version lack a few key features. Anyway, I use mupdf+entr+nvim for many months now and it's more than enough for me.
The web version, for me, is just to share my local project with someone, that's it.