Each player gets a class and domain as part of their title, so logically, these should all play differently.
Now we don't know exactly what most of the elements or classes can do so I've guessed at a lot, you may have better ideas though.
I figure most of these powers are dormant or weak until later levels, maybe even uncontrolled, then at god tier you get ultimate versions of them.
The ideas so far are basically a random mishmash of what I think would be appropriate, some tie into a team setting, some not so much, but they're a starting point.
Classes
Heir - a heir might not be in control of his own skill tree, instead being awarded powers or upgrades at random. In return they might activate more often in battle.
Seer - A seer should be able to spot weak points, or secrets in a level, as well as find more Lore and unique items than other players.
Witch - You'd probably get a lot of activated abilities as this class, perhaps even no uncontrolled ones - you cast them all at will.
Knight - Seems like a straightforward combat class, but perhaps they get bonuses based on the number of allies they have with them.
Thief - Rather than getting a lot of bonuses, might be able to steal items or attributes from foes.
Page - A page is a support class so maybe when cooperatively adventuring every player nearby gets a stat bonus and the page gets double XP for assist kills.
Maid - A maid should get bonus rewards from quests, but perhaps not as much from combat (unless killing something was a quest).
Prince - Local consorts who recognize the Prince may heap tribute upon him, and the class could find more loot than others.
Rogue - Rogue basically = sneak attack, so they might do 2X damage from behind, or if they approach an enemy from the back they won't be alerted.
Bard - how about an attack bonus in time with a musical motif? Like in Mother 3
Slyph - A Slyph is like an elemental fairy thing, so they might have an elemental form with various bonuses
Mage - This would be a lot like a witch, perhaps the abilities would be more offensive than defensive?
Domains
Time - Time players get the stasis effect where enemies can be frozen in time, additionally, they could recruit a future self to aid them in battle
Space - I think consensus on this is space powers means teleportation, as well as altering things' scale. This could include weapons or enemies.
Breath - This would be the most agile classes- perhaps featuring a double jump or glide maneuver. Also might be able to throw enemies around. Think TF2's Scout.
Light - Being concerned with Fortune I'd expect light to give bonuses regarding critical attacks, or with finding rare items.
Blood - My guess is blood translates to "camraderie" or something so a blood player could recruit followers. Alternatively: health regeneration.
Life - A life player sounds like a healer class - this could extend to resurrection and necromancy.
Hope - A hope player would be the opposite of a Rage player - they get more powerful if they're doing worse - so the lower your health, the more powerful you are.
Heart - I'm going to interpret this as a diplomacy class based around emotional manipulation - be able to inspire allies and terrify enemies etc.
Mind - A Mind player would probably have illusive powers - say, invisibility, summoning a phantom duplicate or blinding foes - think the Spy from TF2
Void - This class could be based on phasing powers - being able to pass through solid objects.
Rage - I figure this is a berserker element - the more damage you deal, the more powerful you get, so it'd focus on long combos or something.
Doom - Doom is probably a direct damage class - A doom player's attacks then should be unblockable (maybe not uncounterable though)
Anyways, these are just basic concepts for how each title might play, some of them I'm less sure of than others.
I think the most difficult thing would be that a lot of combinations - mainly thief classes would require specific effects written for them. Would a thief of time rewind their enemies? a thief of breath suffocate them? How does a thief of void even work?
In addition, things like maid don't seem to lend themselves to playstyles all that well.
Actually a thief of time could rewind enemies until before they were prototyped or something, drastically weakening them...
Just to group a few together:
Mage and Witch are based around activated powers, a Mage's being more aggressive, a witches being defensive.
Knight and Page would be based around interactions with others, knight getting bonuses for allies, page giving them. Maid/Prince might transfer their quest reward abilities onto others too.
Rogue, Bard, Slyph and Thief are classes based around being able to do a specific action. Seer has their vision Xfold, so that might also count.
Seer, Prince and Maid have passive out of combat abilities affecting the world around them.
Heir is kind of the odd one out here with his abilities affecting level progression more than anything
Blood, Life, Heart and Mind are all powers centered on other characters being present
Doom, Light, Rage and Hope are high direct damage powers (light counts due to crit stacking)
Void, Breath and Space are all powers that are good for evasion
This is all rather complex stuff, so I'll leave this initial proposal here.