I suspect delay impacts more slow (or error prone) typists who rely more on visual feedback, whereas fast typists presumably generally rely/trust more just physical feedback.
Even this text box, on HN, is noticeably disconnected compared with, say, DOS on an IBM PC-XT, or your average text input area on early Apple computers, BeOS on a first-gen Pentium, QNX on same, that sort of thing, and that's without applying the linked site's extra latency. Everything, just about, is a bit muddy on a "modern" computer. iOS is the closest thing to an exception and even that's gotten worse over the years.
I've had a similar experience with audio systems - I can play guitar tolerably well even if I can't hear what I'm playing, but >40ms of latency will turn me into a ham-fisted mess.