Saving/Loading Replays

What is the minimal set of data your game needs to play-back a level?

For instance, if your gameplay is entirely deterministic, it is enough to record only the random seed, and the player actions (along with the time they occurred), and insert them back into the game at the right time.

I don't know what you mean by "each game system", but your two approaches are fundamentally identical: find every command that needs to be recorded and execute it in the same way as normal gameplay would. This requires, one way or the other, coverage of all entity types and all their possible actions: there's little difference between a centralized replay playback that calls "existing APIs" of game entities and a centralized replay reader that dispatches more opaque data to games entities to replay their own events.

It seems you are too interested in the binary data and file formats you'll use for replays: in practice, you should design a simple text format or a simple database schema (to let you edit replays) or leave binary data to a serialization library.

The serious difficulties are accounting for all possible events, identifying game entities to dispatch replay commands, ensuring deterministic playback and faithful timing, and avoid hardwiring needless details of complex, changing data structures in replay management subsystems.