Great, I'll be keeping a look out on that too: 
I haven't attempted to compile MATE yet - the Wine project is the biggest thing I've compiled. As a rough indicator - you'll need to acquire the source code for each MATE component from:
Unfortunately, the MATE Wiki has been down for some time, but I found this (the original, early version of the project?) with some hints of dependencies and order to build:
Take some of this with a pinch of salt as definitely looks like the early days of MATE.
You'll need to acquire development files via the CentOS' repositories, as well as build tools (e.g. gcc and make) There might be a metapackage to install all the necessary tools - Ubuntu has a package called build-essential . You'll need to find the CentOS equivalent from the Ubuntu/Fedora packages list.
Each project may describe how to build in the README, but usually it's just:
./configure
make -j4 # Change '4' to the number of CPU cores to build faster
sudo make install # Likely installs to /usr/local
If ./configure fails, then it would state what's wrong. Note that 
MATE did go GTK3 only after 1.18.
But, you could run into trouble as CentOS ( 1.16.2) might be like 
Ubuntu MATE 16.04 in that it's still primarily a release based on GTK2. This could mean other applications (and development files) in the CentOS repository are old.
If all does succeed, and you have GTK2 applications that won't scale well at a HiDPI resolution - there may be workarounds:
Before installing any of the compiled files, I'd highly recommend backing up the entire system!
Hopefully that should be the basics to get started. Ask here if you need assistance (it's probably worth creating a new topic). Good luck! 