Thinking that maybe the gcc version is too old I tried using instead CentOS gcc7 development environment (GCC) 7.3.1 20180303 (Red Hat 7.3.1-5) (which doesn't come out of the box). This was an educated guess as c99 is only partially supported in gcc-4.8.5. I have now successfully built:
libgpg-error-1.39
libassuan-2.5.3
gpgme-1.14.0
using gcc 7.3.1. All make check tests have passed.

The json problem can be overcome by changing the configure line to: