I can't unfortunately tell you why the lspci version that's included in ESXi doesn't list the device.
However, what may be worth a try is to run
grep -i "37d0" /var/log/vmkernel.log -A 2 -B 2
to see whether it is detected anyway, and/or install the required driver that's listed in the HCL for your ESXi version, and the adapter's firmware.
André