Hmm, that is indeed a very intriguing question. I agree with Sarah that the answer is yes; however, I think that it is more like "Yes, but..."
The PMBOK 5th Edition section 2.2 defines stakeholders as "an individual, group, or organization who may affect, be affected by, or perceive itself to be affected by a decision, activity, or outcome of a project." By that definition, your competitors certainly qualify as stakeholders!
However, I don't think that most of the typical stakeholder interactions apply. For example, typically stakeholders are involved in defining your project requirements, and you keep them informed of your project progress. If I were developing a product I certainly wouldn't want to either give my competitors a chance to directly shape the direction of the project, nor give them free competitive intelligence on what I was doing!