That makes no sense. In order for someone to have reproductive success it is necessary for them to survive in the first place. Obviously if someone altruistically gives up their life then their future reproductive success is zero.
It's true that, if you don't survive at least up until reproducing, then you can't directly pass on any genes. but surviving isn't sufficient for reproductive success. If you're a sexual animal, and your instincts lead you to survive at all costs, but not to have sex, then your survival is useless, evolutionarily speaking. You can survive as long as you want, but you'll never have any descendants.
In some species, this is particularly evident, like the honey bee I mentioned above. It's not possible for a male honey bee to survive reproduction, and yet their instincts still lead them to reproduce. There are plenty of less extreme examples of animals putting their survival at risk due to their urge to mate - male hippos attacking other male hippos to try and steal their harems at serious risk of injury and death, for example, or birds making noisy or visually stunning mating displays that attract observant predators.
If survival was the only concern of animals, most mating behaviour would go out the window. It's often risky and energetically costly. In a sense, a survival instinct is just a means to an end, the end being reproductive success.
I don't see any evolutionary advantage in what the crow, or the gorilla for that matter, have for displaying what appear to be similar emotional behaviour as humans.
The evolutionary advantages for the crow and the gorilla are the same as they are for humans. All three animals care for their young, so it's essential that parents are willing to put time and effort into this. All three live in social groups, usually closely related (not so much for humans any more - but for most of our time on earth we lived in much smaller societies). This means that the people around you often share many of your genes, and it can lead to indirect reproductive success for you if they succeed at the reproducing game too. Groups that work together cohesively and care for one another are also likely to do better than groups riven by internal division and self-serving behaviour.
All this means that the animals need some way to make them work together and look after their relatives. These are complex behaviours in complex environments, and involve dealing with far too many unpredictable situations. A simple, hard-wired set of strict behaviours, such as least some insects appear to possess, wouldn't suffice. What's needed is an emotional system that biases the animal towards certain behaviours over others, and the systems that get passed on are the ones that, on average, lead to the better outcomes.
So, there's no reproductive benefit to the crow in looking after a kitten. It's a waste of time and resources. The drives which made it do so, however, are the same as those that led the crows parents to survive and raise a healthy chick. It's not an instinct that's been risen above; merely one that's been misdirected.