This is a common saying but i've never liked. The world running on emotions is just another way of saying the world runs on logic, just the premises and goals are different than what we think they should be.
The "set of premises and goals" we currently operate upon are not ours, but planted by someone else (parents, teachers, media...).
Add to all this the fact that world may run however it wants, but the emotions are ours. If we alter the "set of premises and goals" we can alter our emotional response.
If you were to (theoretically) simulate the whole judgement process with all of its real world parameters, including whether or not the judge has eaten lunch yet, the computer would definitely conclude that the result will depend on whether the judge has eaten lunch yet.
However, whether or not it should depend on that is a judgement that the computer can't and won't make.
Because everybody likes tangentially related xkcd: https://xkcd.com/435/
Maybe this is an unfair generalization, but usually when i hear people say something like, the world runs on emotions, its used as an out to avoid having to understand where the other person is coming from, on the [BS] principle that emotions are irrational and unknowable.
Most people have poor self-awareness and don't understand themselves or their own needs.
I also don't believe rationality is subjective but an objective statement about the world. You might not know if someone else's actions are rational, but that has no bearing on how rational they actually are.