From my experience of playing way too much computer games in my youth, the Internet seems to work extremely well for multiplayer games... Of course, if you play against someone on the other side of the world, there will be some lag but that is mostly due to things that are not so easy to change, like the speed of light.
We still have quite a bit of optimizations to make until real-life latencies are limited by the speed of light over such distances.
For any given two points, the shortest distance between them along earth's surface is never going to be longer than half the earth's circumference. Light travels that distance in 67ms:
$ units --verbose 'pi * earthradius / c' milliseconds
pi * earthradius / c = 66.763248 milliseconds
Double that for a full roundtrip time.
In reality, the ping time between myself (in Germany) and the opposite site of the earth (in this case, my company's datacenter in Sydney) is more like 300 ms, i.e. less than 50% of the speed limit imposed by the laws of physics.
Your calculation doesn't seem to account for the fact that light in fibre travels slower than in vacuum, 2/3 if memory serves, so it's a lot closer than you think.
A lot of the latency will be due to the conversion between light and electricity for processing in routers/switches. If we had all optical processing that would probably bring the latency down close to the theoretical limit
67ms each way. My UK-Syd latency is currently 265ms, in theory it could be as low as 112ms if it were in a vacuum. In glass with a refractive index of 1.3-1.5, you’re looking at nearer 150-170ms rtt.
Starlink and similar Leo satellites might even have a lower latency as they use laser via vacuum
