AI has a long history of disappointments, but I think many critics often over-simplify what happened, such as with your quote "1960's engineers overpromised and underdelivered".
In the 60's, AI was the domain of a relative handful of researchers (the field wasn't really sufficiently developed yet to call it engineering), mostly at universities, and very few of them were accomplished programmers.
The sudden availability of computing machines in the 1950's had led to great expectations for automation, particularly in machine translation of natural language, playing chess, and similar problems. You might find some actual predictions of success from those days, but the promises inevitably came BEFORE anyone tackled one of those problems in depth. (Or, they wrongly assumed one success guaranteed another, such as expecting to be able to implement good chess playing after Samuel had so much success with checkers.)
Also, be wary of any claims of "they said", "they felt", "they thought", etc.; retrospective opinions (like this one!) are easy to throw around, while documented evidence of actual predictions by "experts" (those who actually tried solving a given problem) can be much harder to find.
Overpromising and undelivering has always been a symptom of software development, regardless of the specific field where the programming is applied. A major difficulty with AI is that non-trivial problems are beyond the capabilities of most engineers. For example, although Charles E. Grant's answer categorizes ELIZA and SHRDLU as "relatively simple", I'd say that's true only of ELIZA (which most first-year programming students could probably implement without much difficulty). On the other hand, SHRDLU is a large, extremely sophisticated program that most programmers would have a very difficult time inventing, let along implementing. Indeed, two teams of university students couldn't even get the source code fully running again, and SHRDLU-like abilities are still hard to find nowadays, over 40 years later.
Since AI is probably one of the least understood and most intractable problems where computers can be applied, overall I'd say progress in AI has generally been at par for the course. There are still high expectations, and our hardware speed and capacities have increased tremendously since the 60's, but I'd say engineers' abilities and understanding of AI aren't improving all that much, so a holy grail like passing the Turing test is still probably a long way off, and overpromising and underdelivering will probably continue for some time.