It's more complicated than that. Do not assume that simpler animals have fewer genes. Sometimes, very simple organisms have a surprisingly large number of genes.
https://www.nature.com/scitable/topicpage/eukaryotic-genome-complexity-437/
https://www.nsf.gov/news/news_summ.jsp?cntn_id=118530
https://news.harvard.edu/gazette/story/2000/02/why-onions-have-more-dna-than-you-do/
Some genes encode for protein. Some genes regulate or control other genes. A lot of DNA is useless, and is called "junk DNA". In addition to the genome, there is the so-called "epigenome" which is external to the DNA, but contains information, and can turn sections of DNA on and off.
Intellligence is not determined by brain size. Some animals with large brains have low intelligence. Some animals with small brains have high intelligence. More relevant than brain size, is the so-called "encephalization factor" which measures the extent to which the brain is larger than you would naively expect it to be, based on the size of the animal.
Despite the fact that most pet owners imagine their dogs and cats have human intelligence, there have five categories of animals that have cognitive ability, where they can solve certain types of problems in experiments. Here they are listed from most intelligent to least intelligent.
1. Primates - Chimps, gorillas, and orangutans have been taught sign language and simple mathematics. Koko the gorilla used 1000 signs, and understood 2000 words of spoken English. Wild chimps have a simple gestural language. They make and use tools in the wild. Monkeys are less intelligent than apes, but also demonstrate tool use in the wild, such as the bearded capuchin which uses a stone and anvil to crack nuts.
2. Cetaceans - Dolphins and Whales. They have also been taught to understand symbols, and can solve puzzles in aquariums. In the wild, different pods each have their own unique culture, where the adults teach the young different hunting strategies.
4. Corvids - Crows and Ravens. These are the most intelligent birds. The most intelligent is the New Caledonian Crow, which in the wild designs and makes a diverse repertoire of complicated tools for a variety of tasks. The adults teach their children how to make and use tools. In the lab, they can solve complicated puzzles that require multi-step solutions.
5. Psittaciformes - Parrots. Less intelligent than Ravens, parrots have also demonstrated puzzle solving abilities in lab experiments.
6. Proboscidea - Elephants. They are highly intelligent social animals. They can recognize themselves in mirrors. In the wild, they live in multi-generation familes, where teaching and learning takes place over multiple generations.
7. Cephalopods - Octopi, Squid, Cuttlefish. Less intelligent than the other animals on this list, it is astounding that an invertebrate can have any cognitive ability. They have surprising intelligence. They can solve puzzles. Octopi can figure how to unscrew lids, and that you need to turn the lid counterclockwise to open it.
Even though whales and elephants are intelligent, they are less intelligent than humans, despite having larger brains than humans. The New Caledonian Crow are less intelligent than humans but still has frightening inteligence for a bird, despite having a tiny brain, although it does have a high encephalization factor. Clearly brain size alone does determine intelligence.
One of the most mysterious things in the biological world is the intelligence of an octopus.
https://www.scientificamerican.com/article/the-mind-of-an-octopus/
https://www.frontiersin.org/articles/10.3389/fphys.2018.00952/full
An octopus has 500 millions neurons, but most of them are outside it's brain, unlike vertebrates where the vast majority of the neurons are inside the brain. However, it would be better to think of an octopus brain as decentralized, where brain-like activity is taking place throughout its body.
Intelligence is not determined only by the number of neurons of the brain but the architecture of the brain, and also neuroplasticity, which describes how easily neurons can change their connections. It used to be believed that humans lose their neuroplasticity in infancy but we now know that we can retain it throughout adult life. The brains of people who have suffered brain damage are remarkably resilient where the brain somehow reroutes signals around the damage. This neuroplasticity is also somehow related to your ability to learn and retain new skills.
There is no reason to think humans have any more neurons today, or are any more intelligent today, than when our species first evolved 200,000 years ago, when we evolved full human intelligence and sentience. We achived a capacity for abstract thought that made everything after that possible. Once you cross that threshold, you have this capacity for abstraction, so why you do assume that we would continue to evolve to be more intelligent after that? What would it even mean to be more intelligent than that? If you had more neurons, would you have more children? If not, then you are not going to evolve more neurons. A trait is not going to be selected for through Darwinism unless it increases the probability that your genes will be passed on to future generations. That's how evolution works. The vast majority of species on this planet have not evolved to be more intelligent over time which disproves your theory that that is somehow guaranteed.
The public fundamentally misunderstands evolution. I remember Chris Matthews on "Hardball" laughing at Republicans for not believing in evolution, and then, in the same breathe, he said, "Of course God was behind it", not realizing that if you say that, then you don't believe in evolution. A process guided by an external agency towards a goal is called "artificial selection" which was known before Darwin. What Darwin discovered is how the process can happen all by itself, entirely the result of random processes. without a person guiding it, without a goal, which is called "natural selection". If you don't believe in that, then you don't believe in evolution.
You see this widespread misunderstanding of evolution manifest itself in various ways. This is why Oscar Pistorius was allowed to compete in the Olympics despite the fact that he had racing prosthetics designed by teams of engineers to go fast while everyone else had natural human feet that were not designed by anyone. People just implicitly assumed that while Oscar Pistorius' feet were designed by humans, his competitor's feet were designed by God, and therefore he didn't have an advantage. Another example, is UFO believers thinking that it is plausible that aliens could look as similar to humans as the stereotype Roswell gray aliens, while real aliens, that evolved on another planet, would not resemble any species that evolved on this planet. However, if you believed that evolution was a progression to a goal, and humans were the goal, then it would seem plausible that evolution on another planet would arrive at the same destination. This is also why the public is not bothered by the human-like aliens in science fiction.
Ironically, some atheists make the same mistake, where they replace "God" with the omnipotent power of "evolution", where they use the word "evolution" in a similar manner to how Christians use the word "God". They imagine that every characteristic of all organisms was evolved for a reason. They believe that evolution was headed towards the goal, which was us. That is wrong. Evolution is not a progression. There is no goal to evolution. It is not guaranteed that life will evolve more intelligence as time goes on. It is not guaranteed that we evolve more neurons as time goes on. There is no reason to think that humans have more neurons today that when we first evolved.
Lastly, the fact that there are so many definitions of entropy, such as Shannon entropy, Hartley entropy, Rényi entropy, collision entropy, min-entropy, etc., indicates that there is no "good" definition of entropy. It is very difficult to define. It is counter-intuitive. You can't just equate entropy with randomness. It is especially difficult to apply any of these concepts to biological organisms or biological evolution. Creationists take advantage of this confusion to mislead people. Any apparent inconsistency is due to flaws in our definition of entropy, not any flaw in our understanding of evolution.