It seems like there are many apps that can be run locally that use LLMs. Although I haven't used this, I found it on reddit and it's made by a student. https://github.com/theJayTea/WritingTools
Seems like there could be others that are better.
I believe the person you're replying to meant local inferencing. The tool you shared, like most (all?) LLM utilities, is wrapping API calls.
https://github.com/theJayTea/WritingTools/blob/main/Windows_...
IIRC, I think the core of Grammarly is a CL-based pattern-matching system, so it may be even simpler than that.