MATE is a continuation of the GNOME 2 code after GNOME 3 came out. It literally IS GNOME 2 just with a different name.
Cinnamon was also a reaction to GNOME 3 but it is an alternative desktop for GNOME 3 ( and newer ). It is mostly modern GNOME. It was never based on GNOME 2.
The only thing XFCE has in common with GNOME is that they both use GTK. XFCE was originally based on XForms ( the XF in XFCE ). It certainly has nothing to do with GNOME 2.