Easier said than done, and I will spare you the details. Fortunately, I was able to download MS Visual Studio Enterprise 2015 through my institute's subscription to Microsoft Imagine, and then install the Intel Parallel Studio 2017, which includes C/C++ and fortran compilers. So I was ready... ready to compile!
Thankfully, mercifully, David Parkhurst and Laurin Wissmeier have provided this awesome step-by-step guide to installing PhreeqcRM, involving all sorts of exciting things like CMake, which I have no idea how to use, but I think I should. So I followed the steps, and managed to compile it all.