My reading of that output, is that you have 16GB of Kingston ECC RAM installed and running as 8GB in two slots (DIMMA0, DIMMB0, Sync Dual Channel). Look at the top, see where it lists Error Correction Type: Single-Bit ECC ? If you didn't have either BIOS support for it, CPU support for it, or ECC Memory fitted, it would say None there. Try the other methods I suggested and see if you can confirm what you now know
Here is some output from my ESXi host (just the interesting bits) :
Physical Memory Array: #31
Use: 0x03 (System memory)
Location: 0x03 (Motherboard)
Slots: 4
Max. Size: 32 GB
ECC: 0x05 (Single-bit)
Processor Info: #32
Payload length: 0x2a
Socket: "SOCKET 0"
Socket Type: 0x24 (Socket LGA1155)
Socket Status: Populated
Type: 0x03 (CPU)
Family: 0xb3 (Xeon)
Manufacturer: "Intel(R) Corporation"
Version: "Intel(R) Xeon(R) CPU E3-1245 V2 @ 3.40GHz"
Asset Tag: "Fill By OEM"
Part Number: "Fill By OEM"
Processor ID: 0xbfebfbff000307b9
Status: 0x01 (Enabled)
Voltage: 10.1 V
External Clock: 100 MHz
Max. Speed: 3800 MHz
Current Speed: 3400 MHz
L1 Cache: #4
L2 Cache: #29
L3 Cache: #30
Core Count: #4
Core Enabled Count: #4
Thread Count: #8
This obviously being repeated for each memory slot:
Memory Device: #34
Location: "ChannelA-DIMM0"
Bank: "BANK 0"
Manufacturer: "Micron"
Serial: "DEADE43E"
Asset Tag: "9876543210"
Part Number: "18KSF1G72AZ-1G4E1"
Memory Array: #31
Form Factor: 0x09 (DIMM)
Type: 0x18 (DDR3)
Type Detail: 0x0080 (Synchronous)
Data Width: 64 bits (+64 ECC bits)
Size: 8 GB
Speed: 1333 MHz
*Edited again, on account of a brain fart