Is your question about the nature of the story, or the nature of science fiction?
Lots of stories that speculate about the nature of God and questions of the supernatural are classed as "science fiction". Larry Niven's "Inferno", James Blish's "A Case of Conscience", Silverberg's anthology "The Day the Sun Stood Still", several Ray Bradbury stories whose titles escape me at the moment, etc. Many more science fiction stories include religious or theological speculation as elements.
Whether such stories are rightly called science fiction is a debate about definitions that is not possible to resolve definitively. It's not like a question about physics where we could perform an experiment to prove it true or false. Ultimately it's a question of opinion: What SHOULD be included under this heading?
Personally my intuitive feel is that speculations about theology are the same "sort of thing" as speculations about physics and astronomy. People who muse about "what would it be like if we met intelligent aliens" often have similar musings about "what would it be like if people had absolute proof that God exists". Even if you're an atheist and think talk of God is pure superstition, still, I sincerely doubt that psychic phenomenon like mind reading or telekinesis are real, but I nevertheless can enjoy stories based on the premise that they are. (And such stories are often called science fiction.) For that matter, it would seem from what we know about physics that faster-than-light travel is impossible, and yet this idea is fundamental to a large percentage of what is called science fiction.
Further thought years later
I've seen a number of atheists try to come up with theories to explain away the ending, i.e. to say that the ending really is NOT that God brings the universe to an end. But surely the plain reading of the story is exactly that: the monks have fulfilled God's purpose in creating the universe and so God ends it as now complete. If this ending doesn't fit with your beliefs about religion ... so what? When I read a vampire story, I don't try to reinterpret the story to explain away the vampires because I don't believe that vampires really exist. It's a fiction story. I sincerely doubt that Mr Clarke thought the universe was really likely to end this way. I don't know if Mr Clarke even believed in God. It doesn't matter. He was trying to write an entertaining story.
If the ending of the story is inconsistent with your view of reality, it doesn't matter, because no one is claiming that it is anything other than a fiction story. I can't imagine that someone would point to this story as somehow "proving" that there really is a God.
If a story conflicts with your world view, you might reasonably say, "That could never happen of course, but wow, it made a cool story." Or you might say, "That could never happen, and the story was just so unbelievable that I couldn't enjoy it." In some cases you might even say, "Oh brother, the author is trying to push this controversial religious/political/social/whatever idea. Sorry, it just doesn't work for me." But it is just, well, silly, to try to "reinterpret" a story that clearly and obviously means X to force it to mean Y because you don't agree with X.