The people webpart only displays a profile picture if the person has email in office 365. We have clients who are not using email in o365. Their pictures show up in Delve, but not in the people webpart.
We have got news :)
Starting April 2019, we are now allowing 6 different ways of retrieving the People profile picture, including Delve.
Check it out in the picture below and make sure to update your web part to the latest available version.