It doesn't need to be all in the browser. I've put together Linux systems with locked-down Kiosk desktops, and also had no problems at all.
One of those icons is a web browser, but native programs are better where available. Much less bandwidth used, and performs very well on even old slow hardware. Still a locked-down, unprivileged user experience with no way to install programs, or even run anything they haven't been given access to.
Of course it's easier to get started when someone did the work for you, but more difficult when you find you need to do something more than the lowest-common-denominator use-case.