Thanks for excepting my answer, even if it didn't work for you (or did it now?).
Are you sure you entered the correct command for the SystemCaller? It's sometimes a bit a pain to get it right, escaping certain characters and so on... (see documentation).
Anyway, you cannot call this website from FME workbench. It's not an API that would except POST/PUT methods so you can upload something using the HTTPCaller transformer and get a response, but it's made using pure JavaScript (and only allows for models up to 10MB, I noticed in the code).
I guess that's also the best for the Cesium people, else everyone would throw hundreds of files at their conversion service and their site would become unresponsive (or they'd pay a fortune on hosting) ;)
@sander_s thank you for the advise, it almost worked but probably the exe has some bugs, so I wonder if it's possible to run the online translator, which never had problems.
I mean the converter you can find at this link: https://cesiumjs.org/convertmodel.html (it works with a simple drag and drop)