Interesting that it worked for you.
The dialog displays immediately on running the installer. The installer never gets to a point of selecting a JDK.
I have both 32 bit and 64 bit JDK installations, and since you're using a 64 bit version, I've mapped my JAVA_HOME to the 64 bit version. So my "java -version" reports:
Just to let you know I didn't want to stay blocked so I went ahead and installed the zipped version of STS 2.8.0, mod'ed a setting or 2 in the STS config file and got it up and running.
java version "1.6.0_24"
Java(TM) SE Runtime Environment (build 1.6.0_24-b07)
Java HotSpot(TM) 64-Bit Server VM (build 19.1-b02, mixed mode)
However, I'd really like to solve this installer thriller if you're willing as well.