Thought I heard my ears ringing... Blast from the past here.
That's the beauty part of recording server state and playing it back -- we included a recording of whatever accurate integer-based OS time I could get on each platform. On Windows, for example, I record the raw values of QPC ticks and the tick rate into the recording. Then on playback, I play back the clocks themselves as if the hardware has that tick rate and tick count are from the recorded computer. So if frame 10 took 33.3ms and frame 11 took 66.7ms, we'd play them back that way.
Note that playbacks are almost never in real-time. The reason a typical server frame takes 33ms is that we might be processing for 5ms and then yielding the thread (sleeping) for the remaining time during real-time gameplay. On playback, we don't yield the thread, so we play back faster than real-time when doing something like a live Chronobreak (disaster recovery.)
Strictly speaking, you are right. Let's say we had a game with no player inputs (like a bots-only game.) It's possible that the outcomes might vary between two games with the same random seeds if they run different numbers of frames over the same time period. That said, we've actually tried this a few times, and our game code is surprisingly resilient to this -- only in a few instances have we found issues where subtle variations in frame time could impact player outcomes (and those are generally corrected when we find them -- this is an esports game after all.)
A lot of this comes down to tradeoffs. Yes we might have those subtle issues, but if we fixed our timestep, then we'd have the other problem of the game potentially going into slow-motion during (the admittedly rare) periods of long frame times. In practice, we decided time dilation is more negative for player performance than loss of interactive resolution; humans are great predictors of motion with limited information, but they're not so great when the rules of localized reality bend.
Edit: typo