I think (and I could have misunderstood this) that the commands to install the driver can be executed in the console on the ESXi machine - if not as you say, the process wont work. In that case, looking again at the link you sent there are instructions how to include the new driver during the initial install of ESXi - so one other option would be to re-install ESXi and include the revised driver at install time. as you wont have created any virtual machines yet, you wont lose any work.
The VMWare hypervisor (ESX) has always run only on a restricted amount of hardware types. ESXi v4 supports a LOT more hardware than earlier versions. It's really meant to run on server equipment certified to run it. I am actually surprised it works on my hardware.
I'm sure you know this but just in case others don't: There are other VMWare virtualisation engines that run on top of Host OSes (also from Microsoft, Sun, Citrix and Open Source) but these are dependent upon the Host OS (Windows, Linux, Mac OSX, OS/2-eComStation etc.) - if the host OS fails or needs patching, all your virtualised systems get closed down. The host OS in these cases also takes a big "chunk" of available resources. However running on top of a host OS means that you don't have to worry about hardware compatibility with the virtualisation engine as it talks to the host OS not the physical hardware. Some of these packages now take advantage of the chip level virtualisation features to speed their operation.
I looked for a network card after I got the "lvmdriver cannot load error" and indeed having looked at the forums went searching for an Intel Pro/1000 GT card but when I found them costing between AU$90 and AU$250, I decided I'd risk buying the AU$22 Intel Pro/1000 MT card instead, as if it didn't work, I could always use it for another system. I was lucky - it worked straight away.
Cheers/2
Ed.