First of all, I am not a lawyer, so I can not provide legal advise. When you are serious about this, do not rely on legal opinions of anonymous strangers on the Internet. Consult a real lawyer.
There is never zero chance to get sued. You can get sued for anything. Companies sometimes sue people even if they know they can not win. They just do it to shut down competitors or critics by tying them up with legal costs. It's called a SLAPP suit.
But in my experience, the chance to get sued for this is kinda low. You can not copyright basic trivia and you can not copyright information about products. So simply asking trivia questions about other games is unlikely to violate any copyrights.
Not even trivia questions themselves are necessarily protected by copyright. At least that's what an US court decided in 1987 in a lawsuit against the creators of Trivial Pursuit who got caught copying questions from a book. The court decided that since they didn't take the whole collection of questions and instead hand-pick questions from multiple sources, it's not copyright violation but simply research.
However, you still got to be careful about a couple things:
- Do not violate trademark law when you promote your game. For example, when you promote your game as "Fallout Quiz", then Bethesda might feel that this infringes on their trademark for "Fallout" which gives them the exclusive right to create games with Fallout in the name.
- Do not copy assets. For example, if you copy a popular sprite from a game asking the player to identify it, then having that sprite in your game is a copyright violation.
- Do not slide into defamation. When you make games look bad by misrepresenting them, you might invite a SLAPP suit.