IRC as a real-time Internet chat network was always designed to be ultra light weight with the most minimum requirements on the client as well as server sides, which makes it ideal for small devices or where bandwidth is very constricted as there are no graphics, adverts, or algorithms. So yes it even runs on a calculator!
Of course, this also says something about Casio's extendibility, as the trend today is so often to just lock everything down.
fxIP is an open source TCP/IP stack and IRC client for Casio fx-9860/9750 calculators.
TCP/IP for Casio fx-9860 graphical calculators (with SLIP support, uIP stack) - Manawyrm/fxIP