There is surely a version for Linux. I have been using it in my computer with Archlinux [1] for a couple of years with vim (there are at least two plugins [2,3]). It works pretty good. The only thing is that when running it locally it kind of uses a lot of resources. So not so good when you are with your laptop running on battery.

[1] https://archlinux.org/packages/community/any/languagetool/ [2] https://github.com/dpelle/vim-LanguageTool [3] https://github.com/rhysd/vim-grammarous