The straws grab to the strings on the up and slip on the down. As you observe, look at the angle of the creature and especially the straws in relation to the string. When the straw is parallel it slides easily on the string. There is very little friction. However, when the straw is not parallel to the string it grabs the string. The ends of the straw rub the string and produce lots of friction.
The alternate tilting of the creature is caused by both pulling taut of the one string and the pulling from above of the other string.
Friction is both our friend and foe. In a car, we do not want friction where the engine parts slide against each other. Friction there reduces engine efficiency and wears out the engine quickly, so we use engine oil to reduce friction. On the other hand, we want traction (a kind of friction) in the tires so we don't slide around on the road. Rubber, which is what car tires are made of, makes lots of friction as it rubs against things.