Well, for one thing, even if a gene is highly conserved, you can still measure evolutionary relationships independently of that by using the "third base pair wiggle". (In most cases the third base pair in a DNA codon is redundant in terms of coding the appropriate amino acid in the resulting protein, so changes in it are relatively unconstrained.)
In any case, this variability in gene evolution rates helps in many ways.
For instance it generates more testable predictions for evolution. If we find a gene that's highly conserved in both fish and humans, for instance, it should also be highly conserved in any animal more closely related to humans that fish are, for instance chickens. Similarly if a gene is NOT conserved in both chickens and humans, then it should also not be conserved in fish. Finally humans and chickens should share numerically more conserved genes than either does with fish. (All these predictions appear to have borne out, btw, in the research described in the article!)
Even better, these deductions from evolution (common descent) provide useful information for other areas of biology. If evolution (common descent) is true, and if genes, as deduced by comparisons between species on the assumption of common descent, evolve at different rates, THEN THERE MUST BE A REASON. (If "goddidit" then no reason is necessary, and therefore inferences from such reasons or mechanisms are unavailable.)
So if we find genes that vary very little across wide phylogenetic distances, then the functions of the proteins coded by such genes must also be highly constrained visa vis their primary sequence (the linear sequence of amino acids). This information can very useful in analyzing the functions of such proteins, and in analyzing the metabolic functions they're part of.
Many, many more inferences are possible. For instance say we find a gene that is very similar among almost all vertebrates, except say Birds. Again, if common descent is true then there must be some reason for this. This automatically clues us in that the biological process associated with this gene must be different somehow in birds. It's either become less constrained or there has been a functional shift. (And then we can look at comparisons within birds to see which of those explanations is more likely.)
Here's the only real meaning for genetic similarities. If the genes are very similar or the same, the biological process associated with this gene is very similar or the same.
If the genes are not the same, the biological processes are not the same.
No evolutionary descent 'relationship' is indicated. It is *imposed* by the initial assumption (i.e., that common descent is 'true').