Kickboxing utilities all the major muscle groups. Along with its aerobic and anaerobic benefits, it makes a total full body workout.
Let's look at the particular muscle groups used.
The left jab begins with elevation of left scapula and involves upper traps 1 & 2, levator scapulae, and rhomboid muscles. Flexion takes place using mainly the pectoralis major as well as medial rotation using mainly the pectoralis minor, anterior deltoid, and latissimus dorsi muscles. The elbow joint is extended using the triceps brachii mainly. The arm is pronated at the radioulnar joint using the pronator muscles. The right internal oblique and left external oblique also come into play when torso rotates and laterally flexes to the right as a result of the throwing punch with force.
The lead foot in most cases should step forward as the jab is being thrown with the rear foot providing a 'push'. Immediately after the jab is thrown, slide the rear foot forward to close distance if needed
The right cross punch begins with elevation of the shoulder involving upper traps. The levator scapulae mainly. The same exact same movements occur simultaneously except using the right side of the body. However, the incorporation of the lower body makes this phase the 'power' phase.
The movements of the lower body are synchronised with those of the upper body simultaneously in creating a very forceful punch.
Starting with the right hip joint, medial rotation takes place using mainly the anterior portion of gluteus minimus and tensor muscle. The knee joint then flexes. The right ankle joint then is in flexion.
All of the upper and lower body movements occur simultaneously and is a whole movement that takes a lot of practice to get perfect.
Throwing the left hook begins with elevation of left scapula in the shoulder. There is very slight protaction of left scapula. Next, there is abduction at GH joint bringing elbow and arm up high by eye level.
Elbow is in flexed position and really doesn’t extend. Horizontal adduction at left GH joint using pectoral muscles and deltoids is what mainly puts arm through striking motion with elbow joint locked in flexion.
All these movements occur within quick succession of one another. The right internal oblique and left external oblique are used in rotation of torso to the right. The lower body is also incorporated into this phase to make it more forceful. The left hip joint is medially rotated using the anterior portion of gluteus minimus. The knee remains in a flexed position. At the ankle joint there is plantar flexion using mainly gastrocs and soleus.
Of course this is a pretty detailed breakdown. Even pro boxers spend much time practicing, perfecting and honing there skills. Timing and coordination and defence is key when executing any strike.