By only concidering the following text, how can one say that it is Christianity that the speaker is talking about?
"The present life of man, O king, seems to me, in comparison of that time which is unknown to us, like to the swift flight of a sparrow through the room wherein you sit at supper in winter, with your commanders and ministers, and a good fire in the midst, whilst the storms of rain and snow prevail abroad; the sparrow, I say, flying in at one door, and immediately out at another, whilst he is within, is safe from the wintry storm; but after a short space of fair weather, he immediately vanishes out of your sight, into the dark winter from which he had emerged. So this life of man appears for a short space, but of what went before, or what is to follow, we are utterly ignorant. If, therefore, this new doctrine contains something more certain, it seems justly to deserve to be followed."
The other elders and king's councillors, by Divine inspiration, spke to the same effect.
In a sense, you are right to ask this question. There is nothing specifically from the text itself that we could point to in order to prove that it is refering to Christianity as a religion. However, the text clearly is prompting the reader to be very aware of the ephemeral and transitory nature of his existence and to try and live his life accordingly. The text therefore picks up on an important tenet within Christianity, which is a religion that urges its adherents to live their lives not for this life but for the world to come.
My first response would be the writer's reference to the sparrows, which are creatures mentioned in the Bible:
Are not two sparrows sold for a penny? Yet not one of them will fall to the ground apart from the will of your Father. (Matthew 10:29)
One source notes that sparrows are referred to in the Bible at least seven times. The quote about speaks to the importance of sparrows to God—in that man is as much of a concern to God as mere sparrows.
The second item that stands out to me is speaking of the life of man and its temporary nature. Rarely does the secular world speak with concern over the length of life for a man. And there seems a very spiritual sense to knowing the before and after—a lofty thought in a secular world, but something with great significance for a man (person) of the Christian faith.
So this life of man appears for a short space, but of what went before, or what is to follow, we are utterly ignorant.
The reference to Christianity here is mainly implied, although the paragraphs that precede and follow this passage make it absolutely clear that the "new doctrine" mentioned here is in fact Christianity. The reference here to "divine inspiration" also strongly implies a Christian context.
I think you can also interpret this to mean that our time on earth is fleeting, and we will spend much more time in Heaven. Heaven, should we go there, is more important and we should be less concerned with being on earth than being in Heaven.
I suppose that you could say that the idea here is that being Christian gives you certainty about what comes after you leave the hall like the sparrow. It gives you certainty about existing in the next life.
However, I don't really see how that is unique to Christianity. Most religions have some afterlife that they are sure of. So I'm not completely convinced by what I'm saying, but that sounds better to me than anything else I can think of.