This is a great question as it touches on the history-in-the-making, a revolution in molecular biology taking place in our lifetime. In the last two decades the "central dogma" of molecular biology, formulated by Watson and Crick after the discovery of DNA in 1952-1958, has been overthrown. The neat picture of genes, exclusive containers of hereditary traits, coding proteins and having the code transcribed by enzymes and then delivered by messenger RNA from the nucleus to the ribosome, where it is further transcribed into amino acids; has been replaced with a much more complex, and messier, picture of epigenetic suppression and modification of the code, directly influenced by environmental factors, and regulated by vast swaths of non-protein-coding "DNA elements" (new inclusive term, replacing "genes") previously dismissed as evolutionary "junk".
The recent papers mentioned in the OP derive from the simultaneous publication of 30 (!) linked articles on September 5, 2012, in Nature and several other journals, by the Encyclopedia of DNA Elements (ENCODE) consortium authors. They mark a major advance in deciphering the "junk" DNA functionality. ENCODE is an offshoot of the Human Genome Project launced after its completion in 2003. The information dump was so massive that Nature created a special website meant to guide the readers through it, ENCODE also has its own website.
But the idea of active DNA not involved in protein coding, which was its primary function under the "central dogma", but producing non-coding RNA (ncRNA) is much older. A good historical survey on this topic is Eddy's Nature review Non–coding RNA Genes and the Modern RNA World (2001). Eddy traces the idea back to Genetic Regulatory Mechanisms in the Synthesis of Proteins by Jacob and Monod (1961). They were not mathematical biologists, and the paper is not very mathematical, but it is certainly very theoretical:
"The idea that ncRNA would be well adapted for regulatory roles is not new. In the process of defining many of the concepts of molecular genetics, including mRNA and operons, François Jacob and Jacques Monod distinguished “structural genes” (such as lacZ) from “regulatory genes” (such as lacI). At that time, regulators such as lacI had only been defined genetically, and they were known to specifically interact with cis-acting sequences (such as lacO), either at the DNA or mRNA level. Jacob and Monod reasoned that base complementarity would allow RNA to interact highly specifically with other nucleic-acid sequences. They proposed that structural genes encoded proteins, and regulatory genes produced ncRNAs (FIG.5). Forty years later, their proposal is looking more relevant than ever.
One can see from the bibliography in Eddy's review that discoveries of ncRNA genes with epigenetic regulatory functions picked up significantly in the late 1990-s, leading up to an explosion after 2000, when the initial draft of the Human Genome Project was published. The final draft came out in 2003. Some of the sound and the fury of 2000-2003 is reflected in Gibbs's popular review Unseen Genome: Gems among the Junk (2003). But isolated examples were known much earlier. One of the first direct confirmations of Jacob-Monod's speculation came in 1980, due to Rosalind Lee and her colleagues. Eddy again:
"A canonical example of the identification of a ncRNA gene by genetics is the story of the lin-4 regulatory RNA in the nematode C. elegans. The lin-4 locus
was identified in a screen for mutations that affect the timing and sequence of postembryonic development (HETEROCHRONIC MUTATIONS) in C. elegans... The lin-4 RNA inhibits accumulation of the LIN-14 and LIN-28 proteins by an unknown mechanism."
In 1988 Simons and Kleckner in Biological Regulation by Antisense RNA in Prokaryotes described a different type of regulation mechanism effected by genes on the wrong side of the DNA ladder, usually considered to be idle backup copies. From Gibbs:
"In some cases, however, the backup has its own agenda. While the gene is producing a sensible RNA message, its alter ego can churn out an "antisense" RNA that has a complementary sequence. Whenever matched sense and antisense RNAs meet, they mesh to form their own double-stranded ladders -- effectively interfering with the gene's ability to express its protein... These competing RNAs may suppress a gene just by tying up the gene's messenger RNA."
So it is not that epigenetic functions of non-coding RNA genes were not known before 2012, or even before 2000, but rather that they were considered to be flukes, rare offshoots on the highway of evolutionary heredity revealed by the "central dogma", represented by the protein coding by the "true" genes through the three major lanes of messenger, transfer and ribosomal RNA. It is only with the completion of the Human Genome Project in 2000-2003 that the evidence snowballed, especially in humans, and made this view untenable. Gibbs's review describes many other ncRNA regulatory mechanisms that came to light in late 1990-s – early 2000-s, like active pseudogenes, riboswitches, and microRNA. And Eddy sketches the emerging "modern RNA world" hypothesis, meant to replace the "central dogma":
"Many of the ncRNAs we see in fact have roles in which RNA is a more optimal material than protein. Non-coding RNAs are often (though not always) found to have roles that involve sequence specific recognition of another nucleic acid. ... RNA, by its very nature, is an ideal material for this role. Base complementarity allows a very small RNA to be exquisitely sequence specific.
Many functional roles do not require the more sophisticated catalytic prowess of proteins and could be carried out by simple RNAs. Post-transcriptional regulation, in particular, can be achieved simply by steric occlusion of sites on a target pre-mRNA or mature RNA. In cases requiring more sophistication than simple steric blockage, necessary catalytic functions can be delegated to a small number of shared proteins, whereas specific sequence recognition functions are carried out by a horde of individual small RNAs that interact with