I have the same problem with my configuration, basically identical to yours. As far as I can tell the console is in fact attempting to communicate directly with the esxi host on which the given vm resides, which is intentionally impossible in this configuration because we want to keep our hosts completely firewalled off from the outside. The only thing that should be visible is the VS server and it ought to be proxying all communications, including consoles, between the esxi host machine and the VS client.
I can see the VS client attempting to DNS the name of my host, and when I place my client on a network in which this will work, and in which there is a route to the host, all is fine. When the client is outside of that network, and the only thing visible is the VS Server, it's no good.
The fact that dns fails to resolve host names, etc, is not strictly the problem; it is a symptom of this (to me) bizarre behavior of the client attempting the impossible.
Is it not possible to have the VS server proxy the console back to the client? I cannot believe that this is not the defaut out-of-the-box configuration...
Does anyone have a solution to this (other than to RDP onto the VS server box) that does not involve opening ports and providing DNS outside of the firewall for the hosts?
Chris