A command latency over 30ms hurts a lot. And I don't even play competitively. 250ms was not noticed? Absolute nonsense. A quarter of a second is gigantic when it comes to latency.
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!