His death is used to set the tone for the game and help settle us into its weird cardboard cutout aesthetic. He's killed in the game's introduction, with no context or any reason to care about him.
The thing is, we never actually meet Jin – that doesn't happen until the prequel anime Danganronpa 3: Farewell to Hope's Peak High.
It's revealed that the man was Jin Kirigiri, the principal of Hope's Peak Academy and Kyoko's estranged father. But its importance is discovered much later on when Kyoko finds a box full of bones – the same bones seen falling out of the rocket. None of the main characters see this execution, only we as players do.
As the rocket opens, we see Monokuma giggling away to himself as the bones and remains of the man inside tumble out. A man is strapped into a makeshift rocket and fired into space before it unceremoniously crashes back to the ground. The first execution we see in the game isn't given any context until near the end.
