DNA does define an organism in a very real way...but only in the same way that H2O defines water. There is no magical hoo-ha involved with DNA, it is not information in the same sense that language or binary code is information (and I swear to god the next person who says DNA is "binary" or "digital" will be treated like the idiot they are).
I disagree. DNA is arbitary*. There
is a translation step that takes DNA and turns it into meaningful chemistry, with tRNA, mRNA and the other various bits of pieces involved in turning DNA into proteins, it's inert. You could not create a protein from DNA without it, and there is no way to look at a particular Codon and work out which protein it codes for without knowing the cellular systems that unpick it.
* - technically, this is not quite true, there are certain patterns in DNA that make organisms less susceptible to damage through mutation and coding errors, but there are many, many patterns that could satisfy these constrains and only a tiny, tiny number of different coding schemes actually used.