Yes, stretch film is indeed plastic.
Specifically, Stretch film is a plastic packaging material is most commonly made from Linear Low-Density Polyethylene (LLDPE) , which is a type of plastic resin. It is sometimes blended with other plastics like PVC or LDPE to achieve specific stretch and cling properties.
Its purpose is to wrap around items tightly (like on a pallet) and hold them together using its elasticity and "cling" (stickiness to itself).