I don't know if there's a built-in mechanism in NUnit to handle this scenario, but at the very least you can use preprocessor directives.
For instance, create a "Debug x86" solution configuration, targeting x86. Then define the DEBUG_X86 conditional compilation symbol (in the properties of the project). Finally, surround your unit test with preprocessor directives:
#if DEBUG_X86
[Test]
public void Test()
{
// This test will only run when compiled with Debug x86
}
#endif
Edit: Actually, you don't even have to create a new solution configuration, as it's possible to define the conditional symbols depending on the platform (https://stackoverflow.com/a/1313450/869621). So define a WIN32 compilation symbol, and surround your test with it:
#if WIN32
[Test]
public void Test()
{
// This test will only run when compiled for x86
}
#endif