Moriarty started the game with the text "Come and play. Tower Hill . Jim Moriarty. x "

Why Tower Hill ?
Tower Hill is well known in London as the place for public executions . For hundreds of years traitors and criminals have been beheaded or hanged by angry mobs or on order of the crown .
Sherlock must know this.

So the challange, the game is from the very beginning ,a game to the death. How can Sherlock resist?

To solve the final problem , one of them must die .  Reminiscent of the convo in the pool.
Moriarty is challanging Sherlock to Execute , and become like him ( a killer ) or be executed , and all in the spotlight of the public arena.

At the finale of the game , on St Barts roof , Sherlock has failed to execute Moriarty , and he thinks Sherlock must jump so he has won . Hence the boasting  ~ your not like me... your normal ,,,on the side of the angels ( not a killer ) blah blah and gives away that there is a call off code.

Talk about Sir Boastalot .... Moriarty lost because he was boasting , Neat and lol  huh ?

However when Sherlock laughs and turns back to Moriarty and points out he has an out , Moriarty realises that yes , Sherlock will kill him in order to save his friends.

So to force the game to a draw via double suicide, knowing that sherlock must jump , Moriarty shoots himself before Sherlock can do anything to win , and indeed Sherlock does jump .

( Imo the handshake was a signal for snipers to fire anyway , so Sherlock had turned Moriarty's own game against him .So either way Moriary was about to die.)

Sherlock Faking his death however was a cheat .

So who won ! ? Or was it a draw.