I know this sounds like a tricky question as an organization is not a sentient being, so how can it have emotions or the need to manage them? Your organization, small or worldwide, is built by human beings:founders, investors, employees, partners, customers, clients, and competitors. Thus, whether you are aware of it or not, their emotions are running your business. Hence, your organization also has emotional intelligence. An emotionally intelligent organization is one that cares and nurtures for its people and for humankind at large, not only for its profits.
Feeling engaged, feeling excited, feeling motivated, feeling cared for, feeling stressed, feeling overwhelmed, feeling burned out, ...