Having something that behaves close to our real world makes the rules of your game easier to learn for your player, feel more natural, and brings the player to the fun/challenging part more rapidly.
The first time I wanted to have a character jumping in a game, I started using sin(x). The result was kinda akwards: as soon as you jumped off a cliff, you'd end up travelling up and down, as if you'd be riding a curious deltaplane.
The good approach is much simpler and simply require that the speed is increased at every frame by a constant (gravity acceleration) as stated in Newton Laws. Knowing physics makes you find the right solution faster.
It is probably not required to know physics in details when you're doing a game, but it definitely helps, especially if there are some 'virtual reality' features in your game. A game like "From Dust" (Eric Chahi) is essentially physics simulation gamified, while "Another World" only need high-precision capture of real-life motion (so and requires little to no actual understanding of what happens).
It is very likely that inertia and the other bodies motion related fields will be quite helpful to produce something that is pleasant to the eye, even if you're just moving items on a chessboard. Knowing that friction exists helps using it as a game mechanic, even if you don't exactly use their academic version. Same for energy conservation. In fact, I believe we could very much use game development as a way to teach physics.
I'd be very surprised if you ever use Maxwell or Einstein theories, though. But who knows ? Ludum dare could prove me wrong.