You are a tourist visiting London's Kensington Gardens. The nuclear powers of the world are grumbling at each other, and, just as the nukes start flying, you are whisked off to a surreal, fantasy world called the Wabe, modelled after Alice's Wonderland. From the Wabe you travel through space and time to various sites that are (or will be) significant in the history of nuclear weapons.
Trinity has a reputation as a strong story-based game, but I was surprised at how little plot it has, almost nothing. Each of the nuclear locales, except the finale, is like a snapshot in the nuclear story. The locales have a strong ambience, and work together to build a sense of despair. The Wabe balances it by adding some humour with its silliness, although that might well reflect the author's opinion of nukes.
Rather than being a strong story-based game, I found Trinity to be a strong puzzlefest. The challenges are original and very creative. In the realistic locales the challenges are natural. In the surrealistic Wabe, they follow the surreal logic of the place, but they are not just window dressing on abstract logic puzzles. In both areas they sometimes require inspired lateral leaps, and sometimes logical investigation, experimentation, and deduction.
There are issues with sudden death and required resurrection, so you should save often. These issues are common to the era, and it's best to approach the save and restore as part of the gameplay; it's not too annoying if you're expecting it.
The game is structured into three phases. First, a small introduction in Kensington Garden in London, which is an easy start. Then you move on to the Wabe and handful of nuclear themed locales. The nuclear locales might seem like branches, but they are tied into the overall challenge structure of the Wabe phase. You then move on to the Trinity nuclear site for a long finale.
The text descriptions are economical and reserved, with little extended prose or dramatic descriptions. The prose lets the scenes speak for themselves. I think it works well, but fans of purple might find it dry.
Although it might not have much of a plot, Trinity is an experience. It can be tough and frustrating at times, but it maintains a sense of engagement with the game world, motivating you through the difficulties. At the end, you feel like you've had an adventure.