The utility in question is called ProjectorView Global+ and is indeed listed on the page you linked and the 7800 is not listed as being one of the supported models.
We all know mfrs, even the best ones, have to go through admin red-tape internally to get websites updated and maybe the 7800 never got added in so its listing absence doesnt mean it isnt supported, especially as other evidence points to the contrary.
Funnily enough, the 8000 which just came out @ CEDIA 2012 and isnt even available to dealers yet, is already on the list so go figure.
If you download the manual [linked in the 7800 announcement thread], or just turn to page 42 of your printed copy, you will find the info you are looking for.
And lastly, if you are still in doubt, a little bit of reverse-inference:
If my 7800 doesnt support this software, then why did they go to the trouble of installing network functionality into it ?
Now, keep in mind the software might not be able to help you in determining the f/w version but its free so no harm in trying.
Personally, I would contact jimmyj2 for more details about which Mistu office he called and call the same people to see if they will fix it for you or if they can advise your local Mitsu office on how to do it.