My questions to you would be... Do all the contacts actually have emails, or only the ones showing emails?
Also, on the Samsung Galaxy S6 there are various ways to store and to display contacts. Contacts can be either saved in Google Account, Samsung account, Sim card, device memory and be stored even when using special apps elsewhere. So it is possible that the contacts you are viewing are showing their email info due to their location rather than them missing.
In order to view contacts from only one source, you must set the appropriate settings. To display only your contacts on the Samsung Galaxy S6 (ones stored on the phone only).
1. Go into the menu and then into the "Contacts" app.
2. Next select, in the overview of your contacts, at the upper right corner, the "More" button.
3. In the window that appears tap "Settings". On the next menu tap "Contacts to display".
From here you can select from which location you want the contacts to be displayed in the contacts list. Whichever you choose to show is all you will see after this. Unless, of course, you leave it to show all sources.