If you're going to specify that the number of players is 2, there is no advantage over the much simpler system of:
Flip one coin. If heads, player A is the winner. If tails, player B is the winner.
Flip one coin. If heads, player A is the winner. If tails, player B is the winner.
But apparently the constraints are: every player rolls one die once.
That doesn't eliminate the natural scheme, it just adds some useless die rolls. You can have each of two players flip a coin and choose player A when player A flips heads or player B when player A flips tails.
The most pragmatic would probably be to shuffle N cards from ace(one) through N - and let everyone draw).
But that doesn't involve dice.