No, the use of outwit by this character is one game effect regardless of who it targets. And if outwit specified once per game per character, you also would never be able to outwit both Superman and Batman with the same character in the course of one game.
If the effect says once per game, it is limiting you to once per game. If you can make more than one relic roll per game, each roll must by definition not be the same effect. If it's not the same effect, there is no reason you couldn't do each effect once as a free action.

Then you're saying the Relic Roll comes from the Relic itself? That could be. But should the source matter at all? If I have Outwit on my dial and Outwit through Superman Enemy TA then would they become different effects? Outwit from Power being one effect, and Outwit from Ability being another? Your thought process and documentation is fairly sound though. I went from 90% sure to not really sure at all now. Deputies?

Sure, the relic roll game effect comes from the relic, but if there was a character that had something that granted them the ability to make a relic roll, they would be granting it to themselves rather than the relic (because ignore duplicate game effects and all). So the source doesn't really matter.

And to my understanding, outwit on dial and outwit from SE team ability are still considered the same game effect, but one is ignored because of the rule of ignoring duplicate game effects. Having both does not let you outwit twice, meaning they must be inherently the same game effect, or it would be allowed. It is also to my understanding if I were to outwit a power and then lose outwit on my dial but retain SE team ability outwit, the outwit would not end and the same power would continue to be outwitted by that same figure.

Your understanding on this is incorrect. Even if you still retain the use of Outwit in general, the particular Outwit that you used was lost and its effect will also be lost. This is no different then going from regular Outwit to special Outwit on a characters dial. Also, SE doesn't just grant you Outwit, you need to give the character a free action to get the use of Outwit. So you wouldn't even retain the use of Outwit at all.

As VP pointed out this is incorrect. I probably shouldn't have used the SE example though, something like Outwit from the IG would've been better. None the less.

It used to be there was no "Relic Roll" instead each Relic described what needed to happen to pick it up. Those were clearly different game effects. I feel like when they went to Relic Roll that it became the same game effect. But I could be wrong.

So... I'm just going to hope a Deputy lets us know. Not a real pressing issue I don't think as it's not super likely. Not terribly unlikely, but not real common either.

There's currently a way to get three rolls in one turn if you can do it as multiple free actions. Not pressing and not a game breaking thing either but something I'd like to get clarified by an Orange.

Eh, not every analogy is perfect. It had to break somewhere. I think the "needing to take a free action to get the outwit" was pretty close to that point. I do appreciate you and VanisherPunisher correcting my misunderstanding on this issue. That's how I learn.

That being said, if a relic roll for any relic is the same game effect, what let's you violate the once per game rule on that game effect and roll for multiple different relics as power actions?

Why only 3? Run 30 of The Zombie and Splitlip, put all of the Amulets in the same square, you have a situation that may or may not lead to up to 30 rolls in a turn!

My opinion? Because the INTENT is "Once per game, per Relic." We have a lot rulings that seem to operate off intent instead of the actual wording we have.

Actually if you can get the Figure on top of a Relic without using one of your actions
( Team Ability, multiple Sidesteps with a Carry, etc )
and then have another Figure (or even two) with Free TK,
then Splitlip would let that Figure roll to pick up Five, Six, Seven Relics or more.

Of course, all those Relics can't belong to you.
Clever placement by a partner, or unclever by an opposing is needed.

That is in a 300 point game.

And if it is ruled that a fig can try multiple Free Action relic rolls.

All those relics can belong to you.

Black Witch Prime
And either GF Cosmic Boy / Splitlip and 40 point resource if you want theme or WATX Jean Grey x 2 / splitlip and 30 points of a resource if you don't want theme but an extra TK.

If you can do multiple relic rolls as free actions, you bring in your relics using Black Witch and set them out 5 from your start area. TK Witch to one, free action roll for it. Then TK or move to the second, free action roll, and then if you have a third, go for it and try for it too if you aware using the two TK version.

So after turn one, you could have 3 relics and a resource assigned to Black Witch Prime. You have to make the relic rolls of course, but if you land them she becomes a walking nightmare.

Bumping again for an official word. I know it's not high priority, but I'd still like some clarification.

Weird that this lacks an orange response.

Bumping it up again. Looking for an official response, even if its a "we're looking into it."

Why is one needed?

"A character may not activate the same game effect twice in one twice in one turn with free actions, unless the game effect indicates otherwise." 2013 Core Rulebook, Page 9.

"[Game] Effect: A power, ability, or other rule that can affect a game."

I don't think there is any question that the Relic Roll is a game effect. The question seems to be whether it is a different game effect because it is a different object. I do not see why it would be.

If there was a hypothetical object that let an adjacent character use outwit as a free action, a character (who did not already have outwit) adjacent to such items during one turn would not suddenly be able to use outwit twice in a turn. It's the same logic here.

A wildcard can use a free action multiple times to change the copied team ability because it is explicitly stated as an exception. Relic rolls have no exception.

Also, with the above example of 30 amulets in one square. It is not possible; only one object can occupy a square (Golden Rule 3: The Rule of Occupancy, 2013 Core Rulebook, page 7). I thought I remembered a rule where any attempt to place a new object in a square with an object already causes the new object to poof, but I cannot find it.