ZEngine makes use of Zlib 1.2.1 along with code from Gilles Vollant's unzip 1.0 which is included with zlib in the contrib/minizip directory.
ZLib is available from http://zlib.org.
The Zlib license allows embedding which is done for user convinience (and since zlib is a reasonably stable library).
Files within src/zlib and include/zlib fall under zlib's license and are not part of ZEngine.
For more information the readme from zlib is included in zlib.txt