As Wikipedia states, Event Storming is a workshop based method, a form of brainstorming. It helps to identify use cases and to give teams a better understanding of how certain use cases work.
Its results are often just "sticky notes" on a whiteboard. People often just make a photo of the whiteboard to save the notes in digital form (if they are lazy), or type them into a protocol. In my experience is not a replacement for any well-written documentation or use-case description, which allow the writer to flesh out missing details, remove ambiguities, and write a lot more than just a few words on a paper note. The sticky notes from a session may serve you as a starting point for this kind of documentation or description, of course.
However, whether your organization requires well-written use-case specs for communicating requirements, or if they think this would be a waste of time, is a completely different question. That depends to 100% on your organization, their preferred way of working, the number of people who will be working with this information, the time frames, the complexity of the task and the system you are developing, and certain other factors. This is nothing outsiders like us can really tell you - you have to make this decision based on what you know about your audience and your organization.