If they are just running the servers on ESX(i) then yes you'll just see the console of the hypervisor. You won't be able to access the VMs from there. Do you have a remote desktop connection to them?

You should be able to USB passthrough from the physical machine to the virtual machine. You'll still need the remote desktop part.

Otherwise Remote Desktop and copy to shared USB drive attached to another machine?

Or just use another client machine that accesses the file server files and copy them to your USB on the client machine?

Or just connect directly from the file server remote desktop to whatever you've chosen for your cloud service?

Few ways around this.