Correction:

You -> TMnet Gateway -> Other International Gateway -> Destination

Though it might not be that simple. Your request might be relayed into a dozen or more gateways before it reaches the destination.

A suitable analogy would be you, driving to a friends place, which is the destination. Every junction and/or corner you encounter/pass through could be considered as a gateway. And the only difference here is, the junction decides which route to go to. Not you, the driver.

The DNS server plays its part in translating name-based addresses (forum.lowyat.net) to IP address of the host (202.190.197.145). Then you will connect directly to the IP address received from the DNS server.

Your data transfer to the destination never pass through the DNS server.