That's different to a web app, and a private JRE can be used for applications like that, I deploy private JRE's with my java apps because then the user does not need to install a public JRE which can be accessed by any application and used maliciously. Java along with PDF's and Flash forms the triangle of evil as far as web vulnerabilities are concerned.
No it's a web app. You launch a browser and then connect to a website and after a challenge/response pin it logs me in remotely to my work PC - within my browser. I think it's a rebadged "LogMeIn" or something similar. If the Java browser plugin is disabled then it simply won't connect. It's often a pain but at least the advantage is that I can login to my work PC from any device that supports the Java browser plugin and I have my smartphone handy (the challenge/response pin is on the RSA tool which runs on my phone).