Dinosaurs could not maintain body temperature - we can. Intelligence-wise - there is no contest. We can change our environment, Dinosaurs obviously could not. Early man’s intellectual growth took centuries, we are now effectly doubling our technical prowess every 4-5 years.
Using your analogy that the existing genes are expressed, then it seems that we are ‘optimizing’ the code - which would be the opposite of what we would expect with Entrophy.
Whether we have gained, or lost genetic information over time is really irrevalent. If we lost ‘garbage’, there is really no loss - just efficiency gained. This would be another case where we have disproved Entrophy.
Discounting medical advances (ie. longer life); women are becoming fertile at earlier stages in life today, than even 100 years ago. Puberty is setting in earlier, thus our period of potential reproduction has increased. So, again - this would preclude Entrophy.
Even in geography, Entrophy seems to have no traction. Consider, at one point in time we had a single continent called Pangea. We now have Teutonic plate shift that has pretty much balanced the land-masses around the globe. We went from a single land mass - to a complex set of land-masses that appear to be lumped in a ‘balanced’ sensation around the globe.
So, doesn’t Entrophy seem to be the enemy of God?