Torrential Gearhulk's ability says the following (emphasis mine):
When Torrential Gearhulk enters the battlefield, you may cast target instant card from your graveyard without paying its mana cost.
From the comprehensive rules, casting a card means (in part) "to take it from the zone it's in [and] put it on the stack".701.4 After your opponent selects the card Vraska's Contempt, it is put on the stack as a spell.
Counter target noncreature spell.
Again, from the comprehensive rules, countering a spell means "to cancel it, removing it from the stack."701.5
Since Vraska's Contempt is on the stack, is a noncreature spell, and nothing else prohibits it, you are allowed to counter it using Negate.