Here is a formula for originality: To make something original,
1) Choose a concept at random.
2) Repeat step 1 and mix, or stop.
That's it. Try it! as a fun thought experiment almost guaranteeing a "not been done before" result, fast. Puzzle game about a love triangle between triangles? Shooter about extraterrestrial dolphins harpooning humans? Why not? Original ideas are as easy as Mad Libs, and like Mad Libs they can be funny. But like anything that can be reduced to a formula (not even chemicals, as Breaking Bad attests), this type of originality feels cheap. It is original in the negative sense -- gimmicky, novel for its own sake, contrived, and so on.
I think when we speak of originality what we're really searching for, what we really want, is specificity. Specificity is a form of depth, and all games want depth. Specificity is depth of subject matter. A game that explores a particular subject in detail comes across as original in the positive sense. Rich, imaginative, a labor of love, and so on.
* * *Specificity is inherently challenging because it means you have to explore a topic to a level of detail that is not obvious, and it's difficult to know more about a topic than anybody else.
I just finished reading Journey to the Centre of the Earth to one of my kids and was struck by the specificity of the story. Towns and mountains in Iceland, ancient scientists, types of rocks and minerals, all named and described in detail, lending the book an air of authority as well as its distinct tone. The science may be total nonsense, but you wouldn't know it just from reading, and it doesn't even matter either way because it's a work of fiction. Unless you're Neil deGrass Tyson or whatever you're probably not going to have trouble suspending your disbelief as you read, because the specificity of the work is thorough and convincing.
I think this year's critically acclaimed Gone Home is successful in a similar way, by telling a specific story in a specific time and place. The details are well-grounded, giving the game a sense of richness, and making the environment feel convincing. If you played it I bet you spent a while scanning the VHS tape library as I did. Specific names of things are so valuable! Everything needs a name and a little story. Gone Home is arguably not an original game in the conventional sense, in that the core play experience -- everything from the setting (an old house) to what you do in the game (walk around examining things from a first-person viewpoint) are not out of the ordinary. However, the degree to which the game is invested in its specific ideas is unusual, so even though there are dozens of first-person games with terrific exploration sequences, Gone Home is one of very few where that is the entire focus.
To give a real-world example, an old friend of mine knows in intricate detail the history and all the routes of the MUNI bus system in San Francisco. It's a set of knowledge that seems very bland on the surface but I envy it because it's so specific. If Teddy made games he could probably make an amazing game about managing a municipal bus system (he and I played tons of SimCity and Aerobiz back in the day, besides). A game about managing a municipal bus system sounds pretty awful at face value, but then, so does a game about being a customs officer stamping passports, and yet Papers, Please was one of the best, most interesting games of this past year.
Games made by fewer people I think can have a higher chance of being more specific because there are fewer people on the team to challenge the specificity, to rationalize it out of existence. I'm talking about the little things like Journey to the Centre of the Earth's Icelandic locales. What if the reader doesn't know how to pronounce Snæfellsjökull...? Jules Verne decided to give his reader the benefit of the doubt on dealing with that one. But on larger teams, or teams of any size where this there's creative conflict, there's always going to be the temptation to omit, to compromise, to concede, when it comes to the specific details, to file down all those sharp edges. This may be better for a smooth and pleasant development process but it may be worse for the sake of the game's specificity, and therefore for the sake of the game.
Specificity typically requires research, the more the better (and preferably not limited to Wikipedia because everyone uses Wikipedia). The research can be of a real-world subject or in service of a fictional one. Game of Thrones is a work of fantasy fiction, but its level of detail, from superficial things like clothes and food to subdermal things like character motivations, makes it feel fresh and distinct. It takes place in its own made-up world yet it feels very well researched.
The only other good source of specificity is personal experience. To me the emphasis here is on the personal, or in other words, the private. There are some rare cases like the game Papo and Yo, in which a team can rally around one individual's personal experience and make an interesting game about it. But I also think some of the most interesting aspects of personal experience are unrelatable and truly private, and that this is often why art gets made. If I were to just tell you about the most meaningful experiences of my life, or if I tried to make a game unambiguously and autobiographically about it, it would be the worst, just the most banal cliché bullshit, and you would rightfully think less of me as a person for it. My personal experience is not more significant than yours, and does not warrant sharing.
At the same time, that personal experience is all I have. I remember moments from it constantly despite having almost never documented them and almost never told any of them to anyone including my closest family, friends, and colleagues. I channel those moments in the games I work on, channel them so much and so consciously like you wouldn't believe, and you'd never know it because none of the games I've ever worked on seem to have anything to do with me. The key for me is that I keep it to myself. The only way I can make my work personal is to keep private what's personal about it. We relinquish so much privacy these days that I think there is a sense of strength to be gained from consciously holding onto some, only ever hinting at it. Put another way, the less you know about me, the more interesting I am, the more interesting my stories. This of course is not true of everyone. There is no formula, and this is not advice.