So, traditionally you'd check your dll for dependencies using something like Dependency Walker. .pyd files are just renamed .dll files, so should work fine with this. However, Dependency Walker is mostly full of noise - unless you spot something really obvious (and you can ignore all the API-MS-WIN*, EXT-MS-* dlls straight away) then you might find it easier to enable Loader Snaps (see this old but still relevant MSDN article) which should hopefully be able to tell you which loadlibrary call is failing. Alternatively, you can use Process Monitor (procmon) form Sysinternals to see what files Maya attempts to load when you import the module in to a script. I can't remember if Maya spawns a separate process to run it's python scripts in, or if they're executed in the context of the main maya process. This is important as you'll want to filter events in procmon to just maya / the python executable as otherwise you'll be swamped by them.
Edit: Having looked through the source code there doesn't appear to be much in the way of dependencies beyond the python headers themselves and some standard library includes. I suspect it's more likely that this is compiled with a different version of the toolchain than Maya's Python. In the Python interpreter, you should see a line like this when you start it:
Python 2.7.14 (v2.7.14:84471935ed, Sep 16 2017, 20:25:58) [MSC v.1500 64 bit (AMD64)] on win32
It would be good to see what toolchain was used to compile it (the square brackets bit), and then build the extension from source again with that toolchain. Alternatively, you can try running the setup.py for this module from the project's GitHub page, which if your machine is set up to be able to compile python extensions correctly will build it from source. More details about building c extensions can be found on the Python docs page.