The intriguing world of Muay Thai classes is a realm that has been fascinating enthusiasts of martial arts for centuries. This unique form of martial art, hailing from the cultural heartland of Thailand, is more than just a set of physical exertions. Instead, it's a holistic approach towards health, discipline, and mental fortitude. It manifests itself in the form of classes that are designed to work on several aspects of an individual’s personal and physical development.

One might query the essential nature of these classes. To understand this, let's delve deep into the nucleus of these classes: the Muay Thai techniques and movements. These techniques are underpinned by the ‘Art of Eight Limbs’ philosophy, involving the simultaneous use of fists, elbows, knees, and shins. The techniques are not random, and neither are they a mere arrangement of movements. They are strategically choreographed based on the principles of leverage, body mechanics, and timing, which in turn are deeply rooted in the laws of physics and biomechanics.

The inherent structure of Muay Thai classes is generally divided into warm-up, technique drills, pad work, sparring, and cooling down. The warm-up phase includes skipping, shadow boxing, and stretching, all designed to prepare the body for the intense workout ahead. It is comparable to the pre-heating phase in the process of cooking, where the aim is to prepare the system for what's to come.

Following the warm-up, is the technique drills phase. Here, students learn and practice individual techniques under the watchful eye of an instructor. This phase reflects a pedagogical approach of 'practice makes perfect,' which has been advocated by scholars from various fields such as psychology, education, and social sciences.

The pad work phase is akin to a practical test, where students get to apply the learned techniques on pads held by a partner. The emphasis here is more on execution rather than perfection, much like the practical experiments conducted in scientific research to validate or refute a hypothesis.

The sparring phase is where students get to put all their learning to the test in a controlled fight against a fellow student. It is the equivalent of the peer review process in academia, where the work of one scholar is scrutinized and critiqued by another.

Finally, the cooling down phase is where the body is allowed to gently return to its resting state, akin to the resting phase in the sleep cycle. This is crucial to prevent injuries and promote recovery.

The spatial setting of these classes is typically an open space equipped with a ring, heavy bags, and pads. The temporal element varies, ranging from daily to weekly sessions, with each class lasting approximately 60-90 minutes.

Why should one engage in Muay Thai classes? From a sociological lens, it provides a platform for social interaction and community building. Economically, it represents a form of investment in personal health and physical fitness. Physiologically, it aids in weight loss, muscle toning, and boosting cardiovascular health. Psychologically, it enhances discipline, focus, self-confidence, and stress management.

The trade-offs, however, need consideration. The high-intensity nature of Muay Thai could potentially lead to injuries if not done correctly. This underpins the importance of proper guidance and adherence to safety measures.

In conclusion, Muay Thai classes are not just a form of martial art training, but an intricately woven tapestry of physiological, psychological, and social benefits, underpinned by the laws of physics and principles of human body mechanics. The navigation through this labyrinth of Muay Thai classes, thus, needs a deep understanding of the principles it runs on, making it an intellectually stimulating endeavor.