Nothing personal, but this doesn't make any sense.
Huh? What doesn't make sense? That a gene is a DNA sequence that has a product (not necessarily being a protein)? Why does this not make sense to you? Here's the definition of a gene from a randomly chosen glossary. This one from the Human Genome Project. (emphasis added)
Gene: The fundamental physical and functional unit of heredity. A gene is an ordered sequence of nucleotides located in a particular position on a particular chromosome that encodes a specific functional product (i.e., a protein or RNA molecule).
And the Dictionary of Cell and Molecular Biology gives the following definition for "Non-coding DNA":
DNA that does not code for part of a polypeptide chain or RNA. This includes introns and pseudogenes. In eukaryotes the majority of the DNA is non-coding. Non-coding strand refers to the so-called nonsense strand, as opposed to the sense strand which is actually translated into mRNA.
Now granted you CAN find some dictionaries or glossaries that refer to genes and/or coding regions as coding proteins only, but this distinction is obviously arbitrary and nonfundamental since the code itself, the structure of the gene itself, and the transcription mechanism, is no different between a gene that codes (ultimately) for a protein and one that codes for regulatory RNA.
But if you want to structure your argument solely on semantics, then fine. We'll draw the appropriate conclusions.
It just doesn't make sense what you wrote.