Just a note, you probably want to fix the enemies thing so that there aren't teams. So far, you've created 4 teams against each other, with the fact that "allies" don't mean anything here. In the original version, allies made sense, since, you know, they weren't against you.
But, in this iteration, allies make no sense, since for example, Earth isn't an enemy of Water, so why isn't Water an ally? Is it because Fire is an ally? But, then again, Earth's only ACTUAL ally is Order, which doesn't make sense at all, because in reality, these two are simply a different person with the exact same goal. Which also means that if Fire IS an ally of Earth, then so should Death. Basically, this would create 4 teams of two that are essentially 2 teams of 2 sub-teams each of two people.
Earth + Order vs. Air + Chaos
Fire + Death vs. Water + Life
Since the EO faction and FD faction are not at all enemies, they should BOTH be listed as allies, since it is possible for four players to win. But that doesn't even matter, since, you know, what's stopping Water and Life from being allies with Earth and Order? Nothing! Which is why it's basically four teams of two people.
Now, I'm going to ignore abilities, since they don't matter to me that much, and I'm just going to postulate an idea that'll make this slightly better. It simply involves switching the enemies of four players. I also feel like this change allows Void to be a competent faction, instead of teams ganging up on him.
Earth is allies with Fire and Order. Earth is enemies with Air and Chaos.
Order is allies with Death and Earth. Order is enemies with Chaos and Air.
Fire is allies with Earth and Death. Fire is enemies with Water and Life.
Death is allies with Order and Fire. Death is enemies with Life and Water.
Air is allies with Water and Chaos. Air is enemies with Earth and Order.
Chaos is allies with Life and Air. Chaos is enemies with Order and Earth.
Water is allies with Air and Life. Water is enemies with Fire and Death.
Life is allies with Chaos and Water. Life is enemies with Death and Fire.
This pattern fails on account of the team aspect. I feel no element should be given a teammate that can be fully accounted on. Therefore, my suggestion is this (Please note that the poles may be shifted, in case you wish to have Death be allies with Earth and Fire instead of Fire and Air. This is merely a test example that fixes some of the perceived game flaws.)
Earth is allies with Life and Order. Earth is enemies with Air and Death.
Order is allies with Fire and Earth. Order is enemies with Chaos and Air.
Fire is allies with Order and Death. Fire is enemies with Water and Chaos.
Death is allies with Air and Fire. Death is enemies with Life and Water.
Air is allies with Death and Chaos. Air is enemies with Earth and Life.
Chaos is allies with Water and Air. Chaos is enemies with Order and Earth.
Water is allies with Chaos and Life. Water is enemies with Fire and Order.
Life is allies with Earth and Water. Life is enemies with Death and Fire.
In my example, the elements that is adjacent to yourself are your allies. You each share one enemy, just like the original concept, and so I feel this sticks to how the original game was played. This also makes the term ally make sense. Anyone NOT listed as either can now be rightfully called a neutral.
Now, if you REEEEALLY wanted to expand, you could have three enemies, but that feels problematic, and is much bigger, plus it changes a few things. Plus, it's off-topic a bit.
Just figured I'd try to make the game fit the vision better.