Here are the problems I see:
1. That top is probably particleboard/MDF and not up for the job of supporting the load either at the over hang or the spacing between whatever lumber makes up that box (the middle)
2. The red line with the downward arrows/question mark: that built in bookcase is a big void and its unlikely there is adequate bracing to carry the load downwards.
3. Box with the question mark: there
might be a stud there you could tie into since theres a gang box but you'd need to see how its tied into everything else before determining if its useful.
Would I trust this with that much weight?
absolutely not. I've opened up enough walls to know what the inside of that looks like.
Could it be built to work?
100%, it really wouldn't even be that much work. I'd ditch the built in, cut the dry wall out wider than the length of whatever you go with, add lumber until you've essentially built a wooden stand for the tank in void, cover it back up with new drywall, finish the seams and repaint. If you actually want to do this, theres a bit more to it than that but its a weekend project if you're reasonably handy.