Is "Destination Server" purely used for RTT calculation and Auto Selection node, or does it have an affect on routing too?
'Destination Server' is only used for RTT calculation and auto select mode. But it doesn't affect to the routing.
When I look at the packet dump with Wireshark, it looks like the game server IP is 22.214.171.124, which is registered as an LA IP address. Strangely this IP doesn't seem to change regardless of which game server I get connected to.
When I checked the game packet dump properly, it looks that they're anycast technology to reach the game server. For example based on your game dump file, it points that the game server IP is 126.96.36.199 but this IP is anycase IP so it's not easy that how your packet does pass-through.
If you're familiar with traceroute, I think you can test against to this IP which routers are used to reach there.