Nuance say Dragon is not compatible with 64-bit Windows XP. The installer aborts if you try to install it on this system. But there’s a workaround! Simply follow the instructions found here, but omit the part telling you to change the properties of Audio.exe to run in XP compatibility mode, since you’re already running XP (the blog was written to explain how to run Dragon in 64-bit Vista).

Many thanks to Larry Henry for explaining this workaround.