Bernoulli principle

 Brenoulli's princple  is an increase in flow rate has a corresponding decrease in pressure

This spider rifle works by using the bernoullis principle which is an increase in flow rate that has a corresponding decrease in pressure. So when the air is shot through it causes a decrease in pressure which sucks the spider into the barrel. The same principle used in the spider rifle is the same way airplanes get off the ground. An example of how this principle can be used it observed is that carburetors use this principle to suck gasoline into an engine intake air stream.