I like the storytelling in OP that tries to invent the idea that an amoeba will one day turn into a horse[sub]1[/sub] -- just "not so-s you would notice".
LOL!!
The problem is that the genome does not add in new genes over time[sub]2[/sub] - the prokaryote does not become a eukaryote[sub]3[/sub], the amoeba does not "acquire the genes" to become a multicelled animal[sub]4[/sub] etc --- and the ancient tree dwelling hyrax no matter how much time given - does not become a horse[sub]5[/sub].
Let me try and translate this from Creationist to English.
1. The Creationist straw man is existing taxa giving rise to other existing taxa. Sometimes it's a generic saltational straw man like a dog giving birth to a cat. Sometimes it goes after a specific target like dinosaur evolution with something like a stegosaurus hatching a clutch of ostriches. In this case he's trying to cover a broad swath of evolutionary history and because it would
clearly be rediculous for an amoeba to give birth to a horse, they instead "one day turn into" one. Such a straw man might sound good to the uneducated, but to anyone familiar with what evolutionary theory actually says, amoebas are a genus in the kingdom Protista while horses are a species (actually a sub-species, learn something new every day) in the kingdom Animalia and have been on separate lines since the Ur-Eukaryote more than a billion years ago.
2. Here he probably meant to say "information", but unfortunately said genes. Of course gene duplication happens all the time with all sorts of results from nothing to diseases to functional changes in the organism.
3. Well, we can't know for sure. That said, given the use of an imprecise term (again, quite common for Creationists), it's likely that the LCA of Eukaryotes, Bacteria and Archaea would be most likely resemble a Prokaryote. This is the same situation with have with "humans coming from apes" and "humans coming from monkeys". The LCAs humans share with our fellow primates would most likely have resembled them more than us.
4. Covered in 1. Amoebas and animals share a unicellular Eukaryote LCA. The former did not "{eventually} turn into" the latter.
5. In the Creationist straw man version of horse evolution, the Hyracotherium was not a misidentified horse ancestor, but was a modern hyrax (in this particular case, one of two tree dwelling species), despite the fact that the two look completely different and had completely different dentition.
Hyracotherium and Hyrax