Looks like they took a logical cue from the emulators. The quick save, restart feature was basically the only way I was beating some of those older games. Punishingly difficult.
This reminds me of http://nintaco.com/, a recently released NES emulator with an infinite rewind ability. It is apparently implemented with a mix of save states and a recording of controller input which allows to reduce memory usage by just having to replay the input since the last save state.
I would be curious to know if the SNES Classic uses the same trick, although I suppose they don't need it as they probably don't support going very far back in time.