There's a technique to throwing pies and Moe knew it. You don't take it behind you ear like you are throwing a ball unless your target is only 3 feet away. The target will be hit but possibly with the edge of the pie.
Moe held it at his collarbone with the edge tilting forward. Then a lunging step with the left foot with a stiff-arm push of the pie with his right, imparting SPIN before the release. The spin guarantees that the pie will not tumble, the push was more accurate than a sling and Moe's strong arm could send a pie true for up to 10 feet.
Of course, it's reasonable that this other guy shared duties...after all, Moe was hit with his share of pies!