What offline means in a checker, precisely
The word gets used loosely, so it is worth pinning down. Here it means one thing: when you run a check, no copy of your input is transmitted to us. The rules are ordinary JavaScript that arrives with the page, and they execute against the string already in your browser. Nothing is posted, queued, logged or retained.
That is not the same as a tool that keeps working when the connection drops, although this one does after the page has loaded. The distinction that matters is where the analysis happens: on the device holding the file, or on a machine you have never seen and cannot inspect.
It is also not the same as a model grading a document. A language model has to receive the text before it can comment on it. A rule engine does not, because the rules were written before your text existed.