Apparently, having a bachelor's degree and a job in computer science was enough, under certain policies, to be H1B eligible. that the bachelor degree might have been in chemistry or in art wasn't relevant to the old policy. The new policy articulates that the degree should be computer related.
On top of it, it seems the old memorandum was not properly informing on the real policy. The given example sounds very odd though (apparently only programmers who were working for a company who's specialty was _not_ software were eligible for the 2-year degree rule...).
Computer programmer is not in and on itself a "specialized occupation" with the new memo. You also would need to be either senior or have the relevant degrees.