Hi irvken,
These are not only Chinese fonts, but also Japanese for instance, and korean as well.
For instance, just next to the word "Français" on the web page you indicated, this is Japanese fonts.
On my config these fonts display fine because I have the following fonts installed:
Mikachan, Mikachan-P, Mikachan-PB, Mikachan-PS.
N.B: I can see these fonts using (mozilla-)FireFox which I guess is not much different from Mozilla as far as the fonts are concerned. I can see them in the fonts directory from the Gnome-panel->Preferences->Fonts->...
% apt-cache search mikachan
ttf-mikachan - handwritten Japanese Truetype font
If I remember correct, I simply installed these fonts the Debian way, using:
# apt-get install ttf-mikachan
So, if I were you, to install some chinese fonts, I would start with:
% apt-cache search chin | grep font
Hope this will work for you as well.
Good luck!
Sylvain.