I looked over this NASA report and it seems to me they didn't analyze for traces of organics any of the deep core samples. Is my assumption correct and if yes why wasn't this test considered?
They did, although apparently not on that particular sample and for the analysis that you link to, but the low carbon content was discouraging. No carbon, no organic compounds. Later studies of Apollo Lunar samples have provided some interesting, though perhaps expected results. It seems most of Lunar regolith organics that were found could have been imported to it via accretion of zodiacal (interplanetary) dust particles and meteor impacts.
From ALLOCHTHONOUS ADDITION OF METEORITIC ORGANICS TO THE LUNAR REGOLITH, Thomas-Keprta et al., 76th Annual Meteoritical Society Meeting, 2013 (PDF):
Introduction: Papers presented at the first Lunar Science Conference and those published in the subsequent Science Moon Issue reported the carbon (C) content of Apollo 11 soils, breccias, and igneous rocks as ranging from ~50 to 250 parts per million. These values are unexpectedly low given that multiple processes should have contributed to the lunar C inventory. We estimate the contribution of C from exogenous sources (e.g., cometary and asteroidal dust) alone is ~500 ppm, which is ~4x greater than the reported average. So while the assessment of indigenous organic matter in returned lunar samples was one of the primary scientific goals of the Apollo program, extensive analysis of Apollo samples yielded no evidence of any significant indigenous organic species. We have identified for the first time arguably indigenous complex organic matter on the surfaces of the 74220 pyroclastic beads, collected on the rim of Shorty crater during the Apollo 17 mission.
I'll let you read the rest of the paper from its source, but the analysis was done on same Apollo 17 samples as the ones in the paper that you're linking to in the question. I suspect there were many other tests for organics conducted on them, but this report should answer your question well enough. Apollo Lunar regolith samples were tested for presence of organics.