SDL2 perfectly support XP. even the most antique XP machine is perfectly able to run crispy-doom.
The only trouble with Crispy is its libgcc_s_dw2-1.dll that depends on libwinpthread-1.dll that needs GetTickCount64
You can download an other build of this libgcc_s_dw2-1.dll, try the one included in my dsda-doom build, it should work. I think it was included with MingW64.
If you have drivers problems, try to set
in the crispy-doom.cfg. this is not specific to XP, I had problems even under Win7 with a cheap integrated Intel graphic chip.