Haven't used CentOS7 as much, but CentOS6.x a lot.
The following libraries are required (according to one of the old docs:
openmotif, libXp, libXt, libXtst, libXi, libXmu, libXext, libSM, liblCE, libX11
The ones above are really for the GUI. The installer is 32-bit java, so install both the 32-bit and 64-bit openmotif libraries. The other libraries are usually installed as part of the dependencies (I think Java in particular needs libXtst.so.4, if I remember correctly).
The dsedit and srvbuild utilities are also 32-bit, so need the openmotif 32-bit also to run the GUIs.
For ASE itself to run, you should have the latest glibc and compat-glibc at the correct bitness.
Chris