Chromebooks run on Chrome OS and I think are generally under powered for most 'shop' needs so I don't think that anyone has made any software/driver for them.
To take it a step further. Chrome OS is really designed for "cloud" type of programs. It also forces people to use their own repository and not go outside of that. Kinda like what Microsoft Cloud is speculated to do as well.
I believe that Chrome is based on Linux and most commercial sign software is designed to run Mac or Windows OS.
It is based on Linux (like Android is as well). I do believe Chrome OS does support the Google Play store, so you may be able to find programs in there to run of it. If so, I do believe there is a port of GIMP and Inkscape (full versions) in the Google Play store. Those might be your best bet. Especially if you use the InkCut plugin for Inkscape. That might (emphasis might) drive that plotter. I know it works with my Roland cutter.
There is also WINE for Linux (as well as Mac) that translated Windows system calls to Linux calls. It isn't always 100% on all programs and I don't know if you can get it on the Chrome OS anyway. But I have been able to run 16 bit Window programs all the way up to 32 bit programs about 4 yrs old on it without much issue. Again, don't know if it will actually deploy on Chrome OS though, just something that is available for Linux. The closest Windows equivalent is BASH on Windows. Except WINE is far more sophisticated the the implementation on Windows for Linux CLI programs.