Well, it isn’t wrong per se, it just could be construed as oversimplified. Many of those NTs have lots of other functions. Dopamine is also involved in movement and cognition, but you don’t see the pop-psych press talk about that much.
ETA: However, pop psychology DOES talk about serotonin’s effect, and they definitely mention more than mentioned here. I think this image is to illustrate one specific point.
It is not very clear what it is supposed to be saying, and it may bear some distant relationship to something factual, but, basically, no, it is more misleading than “accurate”.
It appears to be implying that your mood and behavior depends upon the overall proportions of these neurotransmitters in your brain. That is nonsense. What matters to your mental state is precisely where and when these neurotransmitters (and the several others) are present in your brain (something that changes from moment to moment), not absolute or proportional amounts. There is some truth in the notion that, for instance, dopamine is particularly involved in the workings of brain systems concerned with attention and reward, but it does not follow that increasing your overall dopamine levels will make you more attentive or happier.
This. Maybe the best way to put it is ‘This diagram is so simplified as to be very misleading’.