This is an exceedingly difficult text, and most english readers might disagree as its highly contextual. But my read of this extract is that the author is arguing that humanity derives from "acting out time" that is making it into a narrative, a story, a history. That's the enacting part. The enunciated part seems to add that the author believes that the act of telling our stories, of creating histories, is essential to distinguishing humanity from mere biology. Others may take a different view. The author is taking some poetic liberties with the meanings of these two words.

Like the others, I agree this text is not straightforward especially "time suffered", "time enacted" and "time enunciated". It seems to me "time suffered" refers to the (passive?) suffering that the writer thinks animals experience as opposed to "true humans" that take control of time (enact) and take control of their story about time (enunciate). I guess "true humans" control their destiny and control the story of their destiny (i.e. give structure to their lives). Of course lions and tigers pretty much eat what they want, so at least these animals control their destiny in some way. Maybe they don't enunciate (or tell) stories about their lives, but maybe they don't care to either? Maybe they are quite content to just kill and eat whatever walks in front of them! Maybe this is a little bit helpful to you?

It’s dreadful. Ignore these examples.