The answer is that as the deadline nears, the team realizes that they have not made enough progress to meet the deadline. They must work longer hours, start cutting corners, and toss out features at the last minute. All of this is extremely stressful. It's also a cascading problem on bigger projects where this team's product is a subsystem that subsequently has to be integrated into a bigger platform, because they may have broken compatibility at the last minute to make their deadline.
Contrast this with scrum, where the team collaboratively sets goals on a regular basis and regularly monitors the work remaining and the rate at which they are progressing, so that they know early whether they need to start making trade-offs or adding people to the team. As the author notes, this trades peaks of extreme stress for a predictable (and manageable) medium level of stress. But it also ensures a more consistent and panic-free delivery process.
The problem of burnout is a separate issue. Neither scrum nor waterfall offers a solution to burnout---that is up to the team's management. Nothing in scrum prevents a team from taking breaks from sprints, either as a team or individually.