I'd treat this as a Missed Trigger, even though it was announced at the correct time - it was then missed. Handle it like any Missed Trigger, allowing the opponent to decide whether or not to put it on the stack.
This odd scenario is actually a good example of why we want the opponent to have a voice in the outcome: they may want the life loss, they might have
Toil // Trouble in hand and thus want the card draw, or they might just say “nope, not getting that extra card”.
However, there is no such thing as a “partial backup”. There are a few specific instances where you can simply apply a remedy (which probably feels like a “partial fix”, but that term isn't used) - this is not a match for one of those. The player didn't simply forget to draw, he forgot a set of actions.
d:^D