In the general definition, team members are considered to be stakeholders, and that's what many books teach. But in real world project management, when was the last time you heard the word stakeholder referring to a team member? None, I suppose.
Although team members are technically a stakeholders, the term stakeholder, in real life, is never used to refer to a team member, but rather to members of upper management (internal stakeholders) and clients (external stakeholders).
Your definition of stakeholder is interesting, but again, the term stakeholder in its practical definition refers to important people only.