Networking within ESXi is different than it is in VMware Server - with VMware Server you can configure networking so that it acts like a NAT allowinf you to use the IP address of the VMware Server and have traffic carried to the virtual machine with ESXi it is different. In its simplest sense you have a virtual switch (which in you screen shot you have 2 configured). There are three types of virtual switch -
- Internal Only - this is a virtual switch with no physical NICs and allows you to create an internal only network
- vSwitch with one physical NIC - allows for creating a virtual network that also can connect to a physical network
- vSwitch with 2 or more physical NICs - allows for creating a virtual network that can connect to a physical network and provides load balancing and fault tolerance
To the virtual you can connect a vmkernel port which is a virtual NIC that is used for management communication to the ESXi host. The vmkernel port is assigned an IP address.
You can also have a VM Portgroup which is how the VMs will communicate to the virtual network and if available out to the physical network.
So with the configuration I am betting there is no route to the 172.16.0.x network form the 172.16.10.x network configured on the firewall-