I think you are confusing server-side java with client-side java.
Just as you don't need php on your windows desktop to view php pages, you don't need java runtime to view jsp pages. Both php and jsp simply produces HTML pages, which you are view in the web browser.
On the other hand, just having server-side java (java servlet) won't help you if your pages use java applets. Java applets are executed on the client (desktop), and so it is un-related to servlet. You still need a java runtime if you want to view java applets.
Well, "Applets" by definitions are client-side, so you have to have a Java runtime to run it. There is no such thing as "server-side applets;" all applets are client-side. (the server-side java programs are called "servlet.")
If you think about it, it only makes sense - if you have an applet that draws some banner text, the code has to be executed on the client side in order to actually draw the text. A server side java program that continually draw the text and push it to the client is just too bandwidth-intensive and technically useless.