The poem seems to be about what happens in sleep, when the mind keeps working while we lie still. The first lines suggest that night is busy, putting all its effort into an "extraordinary past." The title, "Replay," fits: dreams or memories are being run through again, like footage.
Then the speaker turns to us. We have plenty of that past, but "took no notice of" it while it was happening. There's a quiet regret here, the sense of having lived through something remarkable without paying attention.
The last two lines are the strangest and most striking. "We who miss not having any heart / and wake up dead" suggests a feeling of numbness, of longing for feeling we no longer have. Waking up "dead" reverses the usual idea of waking as coming back to life. Judging by the imagery, the mood is eerie, wistful, and a little sad: the night is vivid, and the day feels hollow by comparison.