Neowin reports a number of old AMD processors from the Athlon X2 64 and Opteron 185 series do not support the 64-bit version of Windows 8.1 due to lack of support for the CMPXCHG16b instruction. Only the earliest AMD64 processors do not support this so the number of impacted systems is likely to be very small, and you always have the option of installing the 32-bit version of Windows 8.1 if you really want to update such an ancient system to the latest version of Windows.
Short story: AMD's early CPUs, i.e. Athlon x2 64, Opteron 185 lack CMPXCHG16b instructions. Until Windows 8 (apparently) MS implemented a software solution into the OS to support this instruction (so I read). Windows 8.1 refuses to install on machines based on those CPUs. Windows 8 works great.
We contacted Microsoft for comment and received a response from a spokesperson. The statement confirms the removal of Windows 8.1 support for these AMD chips, adding:
This was a change done to improve the security effectiveness of Windows by removing code that cannot use instructions such as CMPXCHG16b. Based on our data, the number of affected processors are extremely small, since this instruction has been supported for greater than 10 years.