"Reading about rewards in AI context makes me wonder, why current AI only focuses on the network topology aspect of natural intelligence."
Well, it doesn't. Not at all. It looks as if you conflate one very specific AI techique (deep neural networks) with all of AI. Because that one technique is currently insanely popular and has been widely mainstream reported and hyped that makes it look as if your education in that field did not go beyond reading a couple of mainstream media articles. Also, there's a whole huge subfield in AI which is actually defined by it's focus on learning from rewards, which you seem not to be aware of.
"What about the neurotransmitters like dopamine or serotonine? Could they (or more specific: their effects) be key to an AI that feels more “natural“?"
Not applicable as written, too broad and unspecific. "Not even wrong." Looks like someone with superficial knowledge is just throwing a few sticks into the blue in the hope that someone might be aroused to a reply which competently tries to make actual sense out of it.