Is the requirement gathering method in projects called when a group tries to find a solution for a specific problem by gathering a list of ideas spontaneously contributed by its members?
No. that's called brainstorming.
Requirement gathering is when the process of deciding which functionality and features will be included in the product and in which platform it will run.
To do that you need to ask Marketing what the users want, the Engineers for what is possible to build Product Management for what is the minimum/maximum effect you're aiming to produce, and in what budget.