Neither of the terms “Nucleotide-associated protein” or “RNA-polymerase associated protein” are standard in molecular biology in so far as they are not defined in the reference Gene Ontology. (In contrast, “DNA-binding” is.)
An internet search does not bring up many examples of the former usage (at least) and in those it brings up it is not defined. One can only conclude that it means exactly what it says and no more, presumably because the author has limited information about the function of the protein.(Without the original reference I cannot be sure.)
A “Nucleotide-associated protein” is therefore “a protein that in some way interacts with a nucleotide”. On may imagine that it might bind the nucleotide, but the nature of this binding is unspecified and could be reflect the fact that the protein is a kinase of some sort and ATP (or GTP etc) is a substrate. It therefore need not be a DNA-binding protein, in contrast to the statement in the accepted answer from @AlexDeLarge. In fact the term would most likely imply a mononucleotide-binding protein, i.e. a protein that bound ATP or cyclicAMP or GDP or dUDP etc. If it bound a polynucleotide, this could equally well be RNA as DNA.
Likewise, an “RNA-polymerase associated protein” is “a protein that in some way interacts with RNA-polymerase”. It is more likely that this is a protein that forms a complex with — i.e. binds to — RNA-polymerase, but the fact that the author does not use the term “binding” suggests that he is being cautious because he has no evidence for this. Perhaps both proteins are found in the same immunoprecipitate.