I suspect that this question is really more of a rant than a serious question, but I'll try to give a serious and concrete answer.
Scholarship is a term that is widely used in defining the work of faculty. It includes original research, but also often includes translational research and the creation of survey articles, textbooks, software, and other works. In the engineering fields, the creation of patentable inventions is typically considered to be scholarly work. In some fields, the creation of artistic works (paintings, musical compositions, novels) is considered part of the scholarly work of faculty.
As a department chair, your job would include supervising and encouraging the scholarly work of the faculty and students in the department. With respect to diversity and scholarship, the chair would be expected to promote diversity in the department in hiring, recruitment of students, and the creation of a departmental culture that is inviting and open to traditionally underrepresented groups. You could establish your personal experience and commitment to diversity by referring to things that you've done in previous positions.
For example, "As the chairman of the department at University X, I oversaw the hiring of five faculty members, of which three were members of minority groups. During my chairmanship, the percentage of female students in our graduate program increased from 25% to 45%."
Engagement isn't as well known a term as scholarship, but many universities include "community outreach" or "community engagement" as one of the duties of faculty members. This is sometimes grouped under "service", but it's really quite different from the kinds of service to the profession that most faculty think of immediately (serving on conference organizing committees, editing journals, etc.) This particular position advertisement is for the head of a school of education, where outreach might include activities such as providing in-service training to school teachers.
Again, the applicant is expected to show a commitment to diversity in this area. You might write "In my previous position at University X, I chaired a committee that ran an in-service training program on the Next Generation Science Standards for teachers in Urban School District Y in which 90% of the students are members of minority groups. A new curriculum based on NGSS has been implemented across the district and test scores have improved substantially."