Tons of games seem to do this, mostly RPGs, in a way or another.
Fallout New Vegas has that ghoul cult who believe they're being divinely guided to a place full of radiation where they can live in peace. I believe Fallout 3 also has similar things. In general, all fallout games have this.
Wasteland also has a faction of cultists that resemble fundamental protestant christians.
The Ur Quan Masters (Star Control 2) also does this in regards to some alien races, which have cults but no clear indication of the existence of their gods. You even get to pretend you're the gods of a certain alien race at one point. I believe Mass Effect also has similar examples.
King of Dragon pass also has this. While blessings, magic and related god stuff do actualy work/seem to exist, there's nothing in the game that outright proves the actual existence of said gods.
Spore also does this. You can create a theocratic civilization but you never find any hint of the existence of gods or anything like that.
Some Fire Emblem games (maybe all, can't say for sure since I haven't played all of them) also have worship of gods and temples in them, but no clear proof of their existence. There are dragons and demons and other powerful things, but no explicit evidence of gods. In one game, a very powerful demon even pretends to be a god to cause people to release him with the power of their worship.
Odallus: The Dark Call does mention gods at several points, but due to the plot, its hard to say if said gods arent/weren't just really powerful beings using stuff like the Odallus.
Most of this sort of reaffirms my hypothesis: if there's a religion and there's no evidence that the gods exist (either you meet them, fight them, or your prayers have some sort of result), it's never the religion of the player character. Whenever there's a character or group of characters who believe in a god that can't be proven, it's always some kind of crazy cult.
What I'm looking for (and don't expect to find) is a game world where there is a religion similar to the ones in the real world - a lot of people believe in it, the culture is built around it, the main character takes the existence of the god seriously, and yet there is absolutely not a single shred of evidence that the god exists (and asking for proof is a sign of poor character). Prayers are not answered, magic cannot be gotten from the god, there is no physical form to point to and say "yeah, of course he's real, he's right over there."
The question isn't really whether the god is "truly" a "god" in the way many people believe in a god today. It's whether the religion in the game is founded on nothing more than some guy saying "I had a dream and god came and he's TOTALLY real but also he'll never, ever do anything to directly influence the world, so I can't prove it, but trust me, he's totally real" and the guy writes a book and it becomes a major world power. This does not happen in games, as far as I can find. Somehow, sane, rational video game characters never base a religion on anything but tangible evidence - piss off the god and something bad happens, be nice to the god and you can cast healing spells.
Religions in games seem to be divided into:
-There is a god. She's right over there. Be nice to her or she'll kick your ass.
-There is a god. We pray to him and we get points/spells/healing.
-Some crazy cult-ish or “primitive” (or at least non-human) group believes in a god, but the PC (and the player) knows better than to buy into that nonsense. It's always a “haha, look at the stupid fools believing in a god that isn't real!” sort of situation.
I've never seen a game where there is a religion that the PC believes in, where you base your decisions around possible consequences in an afterlife which may or may not exist, where you never get any confirmation that the religion either is or isn't true.
If in a game there are dragons/demons/genies/whatever with massively super-human powers which are worshipped by humans and called "gods", that's still something with a basis in the game world's reality. "There's a god - he's right over there." The definition of "god" is not important here so much as whether there is a religion based on nothing more than an idea, which the main character believes in but which does absolutely nothing for the character.
By the way, I do have a good reason for asking this - I've gotten a commission to write an article on the topic and I want to make sure my hypothesis is sound before writing it. If there are exceptions, I obviously want to address them. And all that you've posted so far (all of you) has been very helpful at helping me organize my thoughts. So thanks everyone! Keep it coming!