This is not the correct answer.  This is a known issue with this driver and it revolves around the NVM checksum on this chipset and some configurations.  I have had this exact issue with the i350's and i211's myself so can say 100% this driver works through 6u1 build 3380124.

Run the following to install a modified build of this driver to fix this specific issue and you will be good to go.  Lspci will show the card and the non-modified driver simply won't load due to the checksum.  This modified driver simply ignores the NVM checksum allowing the driver to load.

SSH to esxi host and issue these commands (if you don't want to pull down the vib locally):

esxcli software acceptance set --level=CommunitySupported

esxcli network firewall ruleset set -e true -r httpClient

esxcli software vib install -n net-igb -d https://vibsdepot.v-front.de

Reboot the host.

Hope this helps!

Collin