Disclaimer, I'm not a biology undergrad and I only know the basics about muscle movement.
I know that doing a bench press works the chest, and specifically the Pectoralis Major because, well, I feel muscle soreness. However, it is not obvious to me what the Pectoralis Major has to do with extending the arm.
Thinking about muscle contraction, I see clearly how, for example, the Bicep flexes the elbow when it contracts. In a similar way, when the Pectoralis Major contracts you get horizontal shoulder adduction.
But what about the bench press? The majority of the movement consists of raising the arms upwards from a tucked position, and the is little shoulder adduction.