I would be surprised if online games use TCP.
Anyway, physics is still there and light speed is fast, but that much. In 10ms it travels about 3000km, NZ to US west coast is about 11000km, so less than 60ms is impossible. Cables are probably much longer, c speed is lower in a medium, add network devices latency and 200ms from NZ to USA is not that bad.
Speed of light in fiber is about 200 000km/s. Most of the latency is because of distance, modern routers have a forwarding latency of tens of microseconds, some switches can start sending out a packet before fully receiving it.
The total length of the relevant sections of the Southern Cross Cable is 12,135km, as it goes via Hawaii.
The main reason I made my original comment was to point out that the real numbers are more than double what the other commenter called “devastating” latency.
I used to play netquake(not quakeworld) at up to 800 ms lag, past that was too much for even young stupid me.
For them that don't know the difference. netquake was the original strict client server version of quake, you hit the forward key it sends that to the server and the server then sends back where you moved. quakeworld was the client side prediction enhancement that came later, you hit forward, the client moves you forwards and sends it to the server at the same time. and if there are differences it gets reconciled later.
For the most part client side prediction feels better to play. however when there are network problems, large amounts of lag, a lot of artifacts start to show up, rubberbanding, jumping around, hits that don't. Pure client server feels worse, every thing gets sluggish, and mushy but movement is a little more predictable and logical and can sort of be anticipated.
I have not played quake in 20 years but one thing I remember is at past 800ms of lag the lava felt magnetic, it would just suck you in, every time.