This quote keeps on showing up out of context. Edsger and I got along quite well. He loved to be the way he was and pushed it. His friend Bob Barton (the great genius of the B5000 design) was very similar in loving to push buttons and being very critical of the not-quite-a-field that we have. When the U of Utah faculty complained to Dave Evans about Barton, Evans said "We don't care if they're prima donnas as long as they can sing!" This was a general attitude back then. Dijkstra was much more funny than annoying for anyone who had any sense of self. The two biggest problems in our not-quite-a-field were those who listened to him too carefully and those who didn't listen to him carefully enough. In any case, in the research and faculty worlds of the 60s -- where the funding from ARPA was very very different than funding is today -- consensus was not very important: really capable people explored without worrying so much about what others thought (this is hard to explain to people who've grown up in the intensely social and identity seeking world of the last 20 years or so). His comment about OOP (a rather different kind of thing at Xerox PARC than what the term means today) did not bother any of us at all -- it was rather a compliment even (which was also not a big deal) for those of us who liked the way California worked in the 70s. His comments helped when they helped, and they mattered not at all when they didn't.
I often conceptualize programming as a two-dimensional continuum, with Alan Kay on one dimension — flexibility, interactivity, composability, exploration — and Edsger Dijkstra on the other — correctness, efficiency, simplicity. We always need a certain amount of each virtue to make our systems: without enough EWD, we can't get them to work at all, and without enough AK, what they do isn't worthwhile.
Many design choices, of course, involve trading off one virtue against another. But that hardly seems to matter when so many of our current systems are so far from the efficient frontier where tradeoffs are necessary!
Priority is tricky to nail down e.g. the EDSAC was operational a year before the Mark 1 (which actually was not operational until 1949). Because of the "B" Williams Tube which held the two index registers of the Mark 1, many other manufacturers -- e.g. Burroughs -- later called their index registers "B registers". (Also, I think the Univac I and II were successful commercially, and earlier than the 704.)
I started programming in earnest and for money in 1961 mostly in machine code on a variety of machines, and I'm pretty sure that the notions of single dimensional sequential locations of memory as structures (most often called arrays, but sometimes called lists), predated the idea of index registers. This is because I distinctly remember being first taught how to move through arrays sequentially just by direct address modification -- this was called indexing in the Air Force -- and later being introduced to the index register or registers -- depending on the machine.
My strong guess (from above) is that the array as sequential memory accessed by address modification of some kind was a primary idea in the very first useful computers in the late 40s, and that this idea pre-dated index registers.
It would be well worth your time to look at the instruction set of EDSAC, and try writing some programs.
According to this https://www.quora.com/Why-did-Dijkstra-say-that-%E2%80%9CObj... the quote was spoken to Bob Crawford in 1988 or so and appeared in the journal TUG LINES produced by the Turbo user's group, Issue 32 (August September 1989). Bob Crawford is alive, I presume one could ask him but I would rather not even link his faculty page because I am afraid he will be inundated by an avalanche of HN readers.