I can see the connections to Greek and Roman mythology, we've been studying that in English in the past few months. :)
I like this idea, but there is one problem: time.
Two player games are 2 player games, and there cannot be that many lobbies at the same time. The network cannot support it. Therefore, it will be like pvp duels, except it takes about 10 times as long to find a match. I don't think many players will be satisfied with that.
Instead, you can make a few changes:
The game must be 1.8 pvp, therefore making killing easier.
The person trying to stay alive only has a bit of armor, a knockback 1 weapons, a few splash potions of slowness and weekness (lasting 30 seconds each), and 8 ender pearls. They will also have feather falling 1-3, which can be upgraded by buying things with points.
The person trying to kill the other will have the same weapons and armor as you said, with a few 30 second speed I potions, and a fire aspect no damage weapon.
The map will not have any big buildings, and will instead have smaller buildings, slightly hilly terrain with a few steeper high points, and a wall surrounding it on all sides. There will also be no teleport pads nor temples like you described.
These changes must be made for the games to go fast enough to be worth adding. Otherwise, there would not be enough servers and people would take way too long searching for a match.