This is an important realization. Our brain can perceive reasonably fast actions, but our reaction is much slower. Under good conditions we can easily tell a 60fps animation from a 30fps animation from a 10fps slideshow, but the fastest reaction time we can manage is around 100ms (the time one frame is visible at 10fps).
We are reasonable tollerant to latency because our brain has quite high latency, and all our actions have to account for that (for example the point in time where you decide to release a ball you are throwing is very different from the point it is actually released). On top of that, many real-world interactions behave similar to latency (e.g. springs). What throws us off is inconsitent latency, because then we are suddenly not able to predict when to perform an action in order to have the effect at the desired point in time.
The 250ms pure read-react time deals with arbitrary events, but when we can chunk reactions into a practiced technique our precision goes way up, to nearly the individual millisecond: thus musicians can play rapid passages with unusual rhythms in time if they have time to plan and prepare, but they lose this ability if dealing with unusually high latency(extreme reverb, amp across the stage, digital audio with huge buffer sizes). The technique, after all, is based on fast confirming feedback that your execution is correct.
And like you say, "bouncy" latency is even more disruptive. We can adjust to a small and consistent lag, but inconsistency will degrade any level of skill.
> And like you say, "bouncy" latency is even more disruptive
The technical term for this is "jitter". Networking and telecoms people pay a lot of attention to this metric, both for the reasons you cite and because jitter is much more noticeable than high-but-constant latency in voice or video communications.
I guess I could have specified networked over the Internet......
The word "networked" is instead used to distinguish from "non-networked" gaming, which involves playing on a single PC. This could be either a single-player game like the Starcraft campaign, a turn-based hotseat game like Civilization hotseat, or a simultaneous shared-keyboard game like Achtung, die Kurve!
I wonder if the rise of competitive RTS has changed this guideline. In SC2 people will start to complain if their ping to the server is more than about 130ms, and anything above 150ms starts to become painfully noticeable.
In Brood War being able to play on "LAN Latency" was a always a huge deal---to the point that unauthorized third party ladder systems enabled players to play at "LAN Latency" even when battle.net official didn't support it.