We need to ensure below three things to have people picker control in the app.
1. Add div tag and define the properties as per below screenshot in default.aspx under pages folder.
2. Ensure office.controls.peoplePicker.js file is added under scripts folder.
3. Now open appmanifest.xml file from the solution. Go to Permission Requests section and select scope as “user profiles” and select permission as “Read” as per below screenshot.
Hope this will be helpful.