It is likely that the term "operational" is an evolving term largely from the context of programming language and computer architecture as Dijkstra used it. For example in EWD282 (1970) one finds the use of "operational abstraction".
Traces of arguments around a dichotomy of "postulational reasoning" and "operational reasoning" can be found in numerous places of Dijkstra's writing.
In EWD463 (1974) Dijkstra engages with a quote of Russell sent to him by Hoare that states that "The advantages of the method of postulation are great; they are the same as the advantages of theft over honest toil."
By EWD604 (1977) he contrasts work Floyd's and Hoare's work on proving partial or total correctness of a program.
Floyd's approach was still very operational, and he seemed to consider the semantics of his program —as a "working mechanism"— also defined in the case of non-termination. Hoare, who only concerned himself with partial correctness, did not need to talk about termination and his approach is in that sense less operational, less "mechanical".
and later
This is a great advantage, because the question of termination or non-termination is always couched in operational terminology, from which I could now depart: if so desired I can ignore the circumstance that my text also permits the interpretation of executable code.
and finally
The above formal manipulations are not in any sense deep. But I am very pleased. Instead of building my theory upon mechanisms which may terminate or not, I built my theory on texts to which —but I don't need to remember that— terminating mechanisms can be made to correspond.
In some sense Dijkstra feels liberated from considering the actual underlying mechanics/operations of the system and thinks in an abstract formal system, that instead, "can be made to correspond" to a mechanism.
EWD936 as mentioned in the question is followed by more writing by Dijkstra on fleshing out his notion of "operational/postulational reasoning" see also EWD 1012, where the use and praise of "postulational" is referred to E.T. Bell (1940), which likely is the first edition of "The development of mathematics". I do not have access to this edition. However we indeed find that Bell discusses the axiomatization of the early 20th century as postulational method in the second edition.
And it is also contained in his rather controversial EWD 1036. For Dijkstra his view was well grounded on having understood past mistakes. I suspect that his comments regarding "well-identified and well-documented mistake" may well be correctly understood in this sense. The particular type of "postulational" thinking and consequent attitudes towards logic and abstraction in CS teaching that Dijkstra advocated was by no means uncontroversial in the field.
