Fake Intel CPUs?

It's an engineering sample (emphasis added):

Specification Genuine Intel(R) CPU 0 @ 2.5GHz (ES)

For more information, see this Intel page: Information about Intel Engineering/Qualification Sample Processors

Well, you got shipped a newer processor than what you ordered, with a marginally lower clockspeed and a few features disabled. Unless it was a hell of a deal, you might want to yell at the ebay vendor.

To sum up all the things in the comments and a few extra details - various levels of fake processors exist from repacked engineering sample chips, to the lovely, and utterly non functional core i7 920 newegg accidentally shipped a few years ago. You'd notice these are repacked chips, or complete bricks, rather than cunningly modified, or homebrewed processors.

In this case though, you got a newer core i5 2450 rather than an older, slightly faster 2520 which has a few additional features. While some intel processors can be softmodded to unlock additional cache and features, I couldn't find any reference to radical softmodding. While you didn't get what you paid for, the chip you have is probably as it was designed and manufactured by intel. I'd suggest taking a closer look at those chip markings - since they would confirm it. It would be possible, and a little crafty to swap those heatshields, but its unlikely since its too much work.

The product identification utility by intel might be of interest here as well

As noted by DragonLord, the CPU I purchased on ebay is an Engineering Sample.

I have meanwhile received a replacement processor that is actually a genuine Core Intel i5-2520M.

Here are the differences:

1. This one, the system BIOS identifies correctly as an

   Intel(R) Core(TM) i5-2520M CPU @ 2.50GHz
   

   with CPU-ID 206A7.

   So, the CPU 0 part of Genuine Intel(R) CPU 0 was actually NOT an indication that this is the first CPU in the system (as suspected in some answers/comments here), but really part of the CPU-ID given by Intel for this particular (and maybe all) Engineering Sample CPU.

2. CPU-Z now reports (differences marked):

   -> Name           Intel Core i5 2520M
      Code Name      Sandy Bridge
      Max TDP        35W
      Package        Socket 988B rPGA
      Technology     32nm
      Core Voltage   0.752V
   -> Specification  Intel(R) Core(TM) i5-2520M CPU @ 2.5GHz
      Family         6
      Ext. Family    6
      Model          A
      Ext. Model     2A
   -> Stepping       7
   -> Revision       D2
      Instructions   MMX,SSE,SSE2,SSE3,SSSE3,SSE4.1,SSE4.2,EM64T,VT-x,AES,AVX
   

   (I didn't mark the Core Voltage as different since it keeps fluctuating a bit anyways)

3. What do you know? AMT now works perfectly!

I will leave DragonLord's answer as the accepted one, since he figured out correctly what was going on.