Why am I missing git2.h and how do I get it back?
I never installed libgit2, but the following might help:
If your distro's repository contains libgit2, I'll advice to remove what you have compiled before and install libgit2 (binaries) and libgit2-dev (headers etc.) packages from the repo. This will place binaries and sources to the right directories.
Otherwise, try symlinking git2.h to /usr/local/include
It doesn't look like the LIBGIT2 variable took (could you show how you set the variable?) as the extra include directive uses /usr/local/include (which is the default).
The LIBGIT2 env var needs to be set to the prefix where the library was installed, typically /usr or /usr/local. It doesn't look like the library was installed to /usr/local as the compiler can't find it, so maybe you need export LIBGIT2=/usr before running setup.py.