Yes, the screen on the Peloton bike and tread has a video camera! It is in the top center of the screen. However, it is not used for the instructors to see you.
Instead, the video camera allows for you to video chat with friends during the ride. You have the option to configure it so the feature is only available to people you follow, or are friends with. Or, you can set it so you can video chat with anyone on your current ride. You also have option to completely disable the feature.
If you click into someones profile on the leaderboard, you will see the option to video chat with them at the top, near their name. However, they also have to have enabled video chatting for you to initiate a chat with them.