In order to answer this question, it is useful to dissect what the main responsibilities of a manager are and then assess whether the definition fits the role that a manager plays. Managers serve as bridges from senior management to the employees who directly serve customers. They implement goals and strategies that executives pass on to them by offering guidance to groups of employees.
Depending on the demands of specific positions, managers typically are responsible for hiring and training employees, conducting performance evaluations and troubleshooting performance issues, and motivating staff to put their best efforts into their work. They also oversee day-to-day operations, set short- and long-term goals for projects and departments, monitor expenses and budgets in relation to the projects they are overseeing, and report results to senior management.
Effective managers need to have good leadership skills and the ability to communicate well in one-to-one situations, larger groups, email, and social media. They often collaborate with the employees that they work with to be sure that projects are performed effectively and on time.
Now we can get back to the definition in the question. To "focus people towards performance of work duties" would include the hiring and training of personnel, the evaluation of performances, troubleshooting problems in performance, working directly with employees, and motivating them to do better. The goals that managers are responsible for formulating and implementing would be the "desired outcomes."
According to this definition, then, a manager's most basic responsibility is the part of their job that entails working to ensure that employees are effectively performing their tasks. However, it leaves out a vital and indispensable aspect of a manager's role, which is to act as a liaison with senior management. In a sense, the most important responsibility of managers is not just to oversee the work of employees, but it is to act as a link between employees and senior management. It might be worthwhile to consider this aspect of a manager's job when you are deciding whether this definition of a manager is effective and complete.