"Your theme is... 60 Seconds!"
And so the brain storming begins. I feel like anything that doesn't explicitly involve time-travel of some sort will get dinged by the Theme-Adherence police, and besides, time travel is fun.
I've never made a game with time travel before, but it presents plenty of opportunities to do novel things. At the very least, even if the mechanics aren't original, I can do things like make the player character switch from replay to AI-driven if the player interacts with his/her previous self or force players to avoid interacting with their previous selves by avoiding line-of-sight and such. All of this is predicated on Terminator-style time travel, where the player goes back into a previous timeframe and can never return to their original. Minute Physics calls this "new/changed history" time travel and I'd call it 'forked history' time travel. The other form would be self-influencing time travel, where you happen to see yourself from the future coming in to your present.
I tried a lot of architectures. It began with the simplest thing I thought would work: A controller component would record keypresses and emit signals. The parent object would listen for signals on the child component and act as though it were receiving input. This worked, but it was hard to jump to a specific point in time.
The next thing I tried was a 'global manager'. Each actor had a 'get state' and 'set state' method. In record mode, actors would append to their history. In replay mode, they'd pull from history and set state. Things got complicated when it came to handling travelling backwards in time and then interacting differently. It was easy to go back to a time and replay, but it wasn't easy to go back, replay, and record at the same time. That part was necessary if we wanted to see ourselves and interact in tandem.
The third thing I tried was similar to the first. Each actor would be a deterministic function of time. We 'set time' which consists of taking the time and setting state accordingly. Functions are determined as only a function of the current timestamp. That works fine. After playing with it, however, it's really hard to make puzzles for it.
I'm going to try the Tracer-style time travel thing where the player can go back 60-Seconds into their previous state while the world stays as it is. This is closer to the self-consistent/non-branching timeline.
Thematically, I really want to rip off Zero-Wing and do a terrible translation of the plot. Character has a time-travel device that sends him/her back 30 seconds, but it has a 60-second recharge. The player got a lethal dose of radiation and needs to go back to save him/herself. The goal is to get past unity and into the net-time-gain territory. Either a recharge of 29 seconds or a jump of 61 seconds.