MTF Mapper 0.5.2 was compiled using MSVC Express 2013, which Microsoft calls "vc12". The Windows binaries have been linked statically against the runtime, but this does not appear to be sufficient to run MTF Mapper under wine without further tweaks.
For me, running "winetricks vcrun2013" in the console seemed to do the trick. I would say that this is a necessary step to get MTF Mapper to work under wine.
In case you are wondering, without the winetricks step I get the following error:
wine: Call from 0x7b83c506 to unimplemented function msvcr120.dll.?_Trace_ppl_function@Concurrency@@YAXABU_GUID@@EW4ConcRT_EventType@1@@Z, aborting
Let me know if there are any other issues related to wine, and I'll see what I can do.