That's an amusing aphorism from a giant in the field, and it was a reasonable thing to say about the technology of that time, but it avoids, rather than answers, the much bigger question of whether machines could ever think.
What is poorly-posed about the question 'could a machine think'? 'Machine' seems acceptably well-defined, and not in a way that rules out, a priori, the possibility of any machine being able to think, so I'm guessing the problem lies in us not having a good definition of thinking - but if that is what makes the question poorly-posed, then surely it also makes the question 'what is thinking?' poorly-posed, yet people stubbornly persist in attempting to address it.
But "what is thinking?" isn't poorly posed in the case that "thinking" isn't well defined, because it is about establishing and agreeing on a definition.
The approach some people take to answering "could machines think?" is to try to determine an actual subject in the real world to call "thinking" in a way that aligns with common intuitions, which to me seems like a good approach. But many (most?) approaches I've encountered instead just assume personal intuition about thinking is sufficient, and worse, in common with all other askers of the question.
Coming back to Dijkstra's aphorism, you will notice that I was objecting to interpreting it as ruling out, a priori, the question of whether machines could ever think. From your latest post, however, you seem to be saying it would be a reasonable question once we are equipped with an established and agreed-upon definition of thinking.
Then there are those, like Searle and Penrose, who agree but insist that thinking is beyond the abilities of any merely Turing-equivalent device.