PC seems to create an abnormal amoun ...
I've been playing on iOS, and recently picked it up on Steam as well due to the sale.
However, it seems that an abnormal amount of DirectShow filter graphs are created, at what appears to be one per unique audio file. Not sure how your sound engine works underneath, but mixing should be done before creating a graph and sending audio to the input pin.
There is a large overhead just in creating that many graphs, as Windows has to perform DSP on each output pin; not to mention, these sound resources aren't unloaded during runtime and as a result, the graph instances continue to consume resources, leading to recurring overhead.
My guess is also that it's likely that assets are only loaded on demand, rather than preloaded/precached, since these graphs aren't instanced until the sound plays for the first time. This is probably what is causing the massive hitching everytime a new sound is played, which is especially evident during the first few moves of a given turn (on a cold boot of the game)