It's real, but cobbled together from multiple sources. For instance we haven't referred to the "reticular activating system" since maybe the 1980s? They call it the "reticular arousal system" which is either a neologism or maybe a reactivation of the term in the literature. I haven't been active in the area in over a decade.
I'll note that this broadly accurate on a macro level, but the details really matter. There are different cortical layers for instance and cell types and the nature of the signal processing differs by layer. So saying "X connects to Y" is useful in some sense, but provides much less information than you might imagine.
If you look at the source (link on the right edge) it's a page with religious ramblings on how this disproves evolution because our nervous system is set up like a computer or microchip. Bibles quotes and all.
The chart is a great testament to how complicated our biology is and not much else.
This is part of my actual area of expertise. They mis-labeled the locus coeruleus as being "stress". Arousal would be more correct. They also missed Barrington's Nucleus right next to it which controls micturition. Absolute trash.
For example the neurotransmitters listed are by no means all of the transmitters. We're still figuring out how many there are but the number is definitely more than 100.