From SPI.h:
#ifndef LSBFIRST
#define LSBFIRST 0
#endif
#ifndef MSBFIRST
#define MSBFIRST 1
#endif
As you can see, there is no type. The compiler merely substitutes literally "1" for "MSBFIRST". So your code would read, after pre-processing:
SPI.setBitOrder(1)
To know exactly what type "1" is (I'm not sure why you need to know) then you would look up "C++ integer promotion". In other words, how are literal integers handled by the C++ compiler.