I've just had a play with this.
What I did was to take some old-school-MSDOS DIR runs on the C: drive (piped to a file) and used freebie utility KDiff3 to see which files changed before and after. This is a rather empirical approach with no understanding whatsoever of how the software actually works.
In the speech recognition software there is an right-click option to Open the Speech Dictionary, and from there you can add and change words.
These seem to go into a small dat file in
C:\Users\<Username>\AppData\Roaming\Microsoft\Speech\Files\UserLexicons
There's also
C:\Users\<Username>\AppData\Roaming\Microsoft\Speech\Files\UserShortcuts
in the same area which I guess has some other specific speech info.
The other folders which changed (and seemed relevant) were:
C:\Users\<Username>\AppData\Local\Microsoft\Speech\Files\MSASR
and
C:\Users\<Username>\AppData\Local\Microsoft\Speech\Files\TrainingAudio
This latter one seemed to be populated as I was going through the tutorial, and holds a .wav file of everything I said to it! The MSASR folder has some fairly big files in there so I'm guessing it holds most of the information.
It's possible that other files/folders are used which weren't so obviously named!
No idea if you can copy these folders across PCs though.
Incidentally by listening back to the .wavs in TrainingAudio I found out how bad the microphone (or possibly sound driver) on this laptop is; there's a constant buzz in the background so I'm pretty impressed the Speech Recognition worked as well as it did.