The issue is that (1) ISL is not installed and (2) once it is,
pkg-config can't find it. To fix this,
emptiness should be compiled manually as follows:
2) Point the package manager to the isl.pc file. This should be in /usr/local/lib/pkgconfig (but could vary, so double check what gets outputted by ISL's make install). Run export PKG_CONFIG_PATH=${PKG_CONFIG_PATH}:/usr/local/lib/pkgconfig followed by pkg-config --cflags --libs isl. Copy what it outputs.
3) Inside of spatial/poly/resources, run gcc -xc -o ${HOME}/bin/emptiness <output of pkg-config> emptiness.c. In my case, this was gcc -xc -o ${HOME}/bin/emptiness -I/usr/local/include -L/usr/local/lib -lisl -lgmp emptiness.c. After this, the binary should be in ${HOME}/bin/.
4) Add the library path outputted by ISL's make install to LD_LIBRARY_PATH. For me, this was: export LD_LIBRARY_PATH=${LD_LIBRARY_PATH}:/usr/local/lib. You will need to have this in your path every time you want Spatial to call emptiness, so consider adding it to your ~/.bashrc.
At this point, the emptiness binary should execute without any problems, and you should be able to successfully run stuff like ./bin/spatial HelloSpatial --sim.