I took a look at it and made you a nice little product file. The code is unchanged from what you've posted. Users still need to make the 2 template edits.
I played with this for about an hour coming up with a simple if($i = 6) {$pagenavthingy .="<br />";} but it doesn't work that way :/
The way the HTML is coded, it will count the categories and forums as the same thing so:
Lobby (Category)
Forum1
Forum2
That would be 3 loops instead of 1
Which means it needs an extra check... if act as forum = 0 then counter+1.. then when counter = 6, throw in a <br /> and reset to 0. Then clean up the html code and you should be on your way if you care to make it resemble the other site.
Edit: Good lord my spelling is off!