But dreams are real—when you are dreaming, you are really dreaming. But their contents are not (always) true. They are like a movie, which is something you can watch, but the movie’s contents—the actors, and the action, and even often the setting—are not true. This comparison just like is not saying two things are identical, it’s comparing one thing—our life in this case—to an evident particular characteristic of the thing it’s being compared to—a dream in this case. A dream is illusory, but you really dreamed it, and it is this characteristic of being illusory that our life is being compared to. But you are truly living. It’s just that there is something illusory about the actors—they seem like they are truly separate beings, but they have no independent self nature; and there is something illusory about the action—it seems as if there is something happening to you, but your intrinsic awareness (he was teaching the view of Tibetan Dzogchen) is not changed in any way by what is happening; and even the location is illusory—every quality you believe is a quality of the world around you is something that is of you, and not otherwise (for example, you see red, but what you believe is red is just how your eyes perceive what is there).
So our lives are real—we are truly living—but everything that happens in them is illusory in some way. That’s what Chögyal Namkhai said. You only thought he said your life is unreal. He said (that Buddha said) that it is like a dream, and the salient characteristic of a dream is that its contents are illusions—seemingly real while you are really dreaming, but then discovered to have been illusory.
Addendum (to answer Yeshe Tenley's request for a definition in the comments below):
To be real, something must be non-contingent, necessary, simple, and evidenced.
Non-contingent, means that it cannot be dependent on anything else in any way. It can’t be brought into being, caused, or created, for example, and it certainly can’t depend on you experiencing it for its reality.
Necessary, means what it says. What is real must be necessary—like a motor in a car, or a charge in its battery—or nothing works. What is real cannot be an option that one can take or leave, something gaudy to set our car apart from those of others.
Simple, means it is not a collection of parts; it is not a union of aspects—it is not structured in any way. The reason for this is that if a thing isn’t simple then it depends on something else to cause it, or make it, to be, and so it is contingent.
Therefore, what is real is necessarily non-dual.
And finally, what is real must be evidenced. If a thing isn’t directly evidenced—since I am asserting that it doesn’t exist, i.e., it can’t be experienced—if it is just inferred, hypostatized, or hypothesized, than it’s not real.
When I say that something exists, or I talk about existence, I mean that imperience is happening, could happen, or did happen. And that is all I am saying, having already seen that the contents of experience were ephemeral at best and certainly lacked any inherent self-existence, how can I assert that any of it is real?
Please note, imperience is a technical word for me; we imperience a dream, but experience its content.
This is taken from my article, "Reality and Existence" and the longer subject of what I mean by imperience and experience is another article "Understanding Experience" which is very relevant to this question, but a decently long read.