This is a general Runtime problem, not Java-specific.
When I try to install Runtime on my 32bit Windows XP SP3 machine I get the following Windows Installer error: "This installation package is not supported by this processor type. Contact your product vendor."
From http://resourcesbeta.arcgis.com/en/help/system-requirements/10.1/index.html#/ArcGIS_Runtime_10_1_for... I see that my operating system should be supported, I ran ProcFeatures on my processor and got the following output:
Intel(R) Core(TM)2 Duo CPU T9400 @ 2.53GHz
x86 Family 6 Model 23 Stepping 10, GenuineIntel
No Execute Protection: Y
Physical Address Extensions (PAE): Y
Floating point emulation: N
Pentium Floating point errata: N
RDTSC (Cycle counter): Y
MMX Instruction Set: Y
3D Now Instruction Set: N
SSE Instruction Set: Y
SSE2 Instruction Set: Y
This seems to be fine. Possibly a bug in the installer logic, or am I missing something else?