There is obviously somewhere a limit where inefficient typing technique becomes a productivity inhibitor. I'd propose that less than 35-40wpm could be a potential concern. But there are so many other factors that consume your time, that a typing speed gain would be like fitting an 3.5GHz CPU in a 10-year-old motherboard - assuming it was physically possible): All other system components are so slow, that the time gains in the CPU hardly matter.
I scored 60-65 wpm on the test (including inline backspacing to correct errors), forcing the speed beyond that results in one or more errors being left in. I'm not unhappy with my typing speed, at least I've never felt it was a productivity bottleneck.
Of course I could be faster. Let's say I could train myself to be 50% faster. Would it make me 50% more productive as a programmer? Clearly not. I rarely type that much code in one go without long thinking-pause, compilation, test, etc.
I recognise your description about walking into rooms, but while coding, I rarely ever forget what I'm doing - in fact, good programmers excel at tracking this kind of task path in their head while they're creating code. And perhaps it's exactly because you have to shake off this kind of deeply nested contexts that you have trouble remembering non-coding-related tasks like fetching coffee, going to bathroom, etc.