If it did happen the creatures would sometimes become too cautious and stealthy for the player to find rather than dying out.
That's not really how evolution works. What you're describing is differences in behaviour which are largely set by fixed tags like [LARGE_PREDATOR], [BENIGN] and so on. And yes, species that do not fear the player may eventually go extinct just like they did in real life (see the dodo bird or one of many predator-free insular animals really). So, in a way, the presence of a murderous player naturally selects for fearful and fast creatures. Selection just happens at the species level rather than the intra-population level.
At least, in theory. In practice, just like in real life, evolution is largely dominated by random drift. The way megabeasts gradually go exctinct despite having much better fitness (stats) than most other species is almost a textbook example of drift dwarfing selection in magnitude.
Megabeasts go extinct because megabeasts do not reproduce very well. Their stats aren't good enough to make them unkillable enough to compensate for their lack of fertility. Megabeasts are unfit creatures in evolutionary terms, or rather they were fit for the world before civilized creatures with weapons existed that would occasionally succeed in killing them; they became unfit as often happens. Drift has nothing to do with it.
Normally there is a diversity among creatures in their relationship to humans, some creatures are more anti-human than others. If a creature is constantly hunted, the creature develops an inherent fear of human beings, conversely if the creature benefits from human presence it develops an inherent semi-tameness. The reason is that there is an initial diversity among creatures before humans arrive, the human presence selects either for pro-human or anti-human creatures among the population until there is uniformity in attitude according to on balance which is the best option.
How evolution works is that genetic drift creatures diversity in neutral traits than then become important traits as the environment changes. The arrival of humans make their inherant attitude to humans a non-neutral trait. So before the creature dies out, the creature would normally develop a wary attitude to humans and would become harder to find as a result; since the tamer creatures got eaten first.