I had a pitcher go 4 for 4 with 2 HR and all of the RBIs who didn't earn the player of the game a little while backr. He had a mediocre game on the mound (gave up 3 or 4 runs in 7 innings but did get the win), so I'm not sure how much offensive contributions by pitchers really matter.
That said, I think it's kind of a toss up in your situation. It's hard to give a pitcher the player of the game award in any situation where his team wins by 16 runs unless he throw a no-hitter or breaks a bunch of records.
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