This kind of problem with WineX is nothing unusual; in fact I'd be far more surprised if you tried to install something and found that it did
There's a list of supported games on the Transgaming site, a search
for Rallisport shows a working rating of 0.
So to answer your questions, no you should never attempt to install any version of DirectX under WineX, because the whole point of WineX is that it emulates the DirectX API as well as the standard Windows API. Trying to install any kind of drivers under Wine or WineX doesn't work and never will, because Wine is designed to work on top of drivers already provided by Linux.
You can get some idea of what exactly is causing the problem by running wine from a console and reading the output. If for some reason you can't see the output (e.g. the display obscures it), pipe it to a file like
wine whatever.exe > /tmp/output.txt
and then use your preferred software the view the output file. More than likely, it's caused by a Windows or DirectX function that is currently unemulated, in which case there's not a lot you can do about it. Sometimes this can send Wine into an endless loop, which would explain the high CPU usage.