Here is the output I get when I run coreinfo:
Coreinfo v3.05 - Dump information on system CPU and memory topology
Copyright (C) 2008-2012 Mark Russinovich
Sysinternals - www.sysinternals.com
Note: Coreinfo must be executed on a system without a hypervisor running for
accurate results.
Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz
Intel64 Family 6 Model 58 Stepping 9, GenuineIntel
HYPERVISOR * Hypervisor is present
VMX - Supports Intel hardware-assisted virtualization
EPT - Supports Intel extended page tables (SLAT)
According to Intel the CPU does have VMX and EPT support. Why is it not showing up in coreinfo?
You are looking at a virtual CPU since you are running the program from inside a VM. The virtualization itself is not virtualizable, so while the physical CPU has these features, the virtual CPU presented to the VM does not.
Are your sure these options are not disabled in the Bios ?
Also: You have a Hypervisor running so the output of CoreInfo may not be reliable. That warning printed by the program isn't there for nothing. I have seen it mis-report the real config on systems with hypervisors (Hyper-V, VmWare, VirtualBox) before.