I have encountered two separate instances where collaborators have tried to install MuJoCo and have been having trouble with getting MATLAB to run the API from the .mex you provide in the downloadable HAPTIX .zip. Assuming their computer meets specs, the .mex is in the MATLAB path, and they are running compatible versions of MATLAB, the underlying problem is a lack of a C++ runtime library on their computer that is normally included with an installation VS2013. The problem can be solved by downloading and installing the 64-bit version of the VS2013 C++ redistributable packages found here.
Thanks David! MuJoCo uses static linking of all libraries by default, but apparently the mex compiler prefers dynamic linking... I should look into its options and hopefully find a way to link the mex statically. In the meantime, one can download the runtime library as explained above.
I found a way to link the mex with the static version of the Visual Studio runtime libraries in the just-released MuJoCo HAPTIX 1.0 RC. There is a mex-compile settings file where one has to replace "/MD" with "/MT". I don't actually have a computer that has MATLAB but no Visual Studio, and haven't tested it, however the mex size increased so I am assuming it worked...