First, remember the purpose of determining interested parties is not to make the longest list of interested parties but to make the list of the most relevant interested parties.
Second, please check Annex A.3 from ISO 9001:2015? Last paragraph: There is no requirement in this International Standard for the organization to consider interested parties where it has decided that those parties are not relevant to its quality management system. It is for the organization to decide if a particular requirement of a relevant interested party is relevant to its quality management system.
In my opinion, I prefer to frame a particular competitor as an external issue in the organization’s context. However, I also see organizations including “competition” as an interested party. This approach becomes inconsistent when we determine competitors' requirements and expectations. The success of the quality management system does not depend on meeting their requirements and expectations. However, a particular competitor can represent a threat (negative external issue) that combined with the organization's weaknesses, and the interests of customers can result in a major risk.