Well, I found it by looking through a stack of old books stashed in an unnamed and dank corner of the attic.
It's a story that appears in a french science-fiction anthology edited in 1983: "Univers 1983", where it is marked as "inédit", i.e. unpublished as yet.
The short story was re-published in 1989 in another anthology, "La Frontière Eclatée" ("The Shattered Frontier").
It is called "La Vallée des Ascenseurs" (literally "The Valley of the Lifts", which doesn't sound promising). The authors are Sylviane Corgiat and Bruno Lecigne. That duo has written a few novels, none of which I have read or heard of. So the story is originally in french. I don't know whether it has ever been translated. I don't think so.
Seeing that "Tron" (the movie) had opened in 1982, the authors may have gotten some inspiration from that.
From the text, here is the handwaving explanation about the alternate reality. There is no direct link to virtual reality or gaming.
The computerman Conrad, now Sir Conrad, has established himself as king of the city of Bass-Einf as he can perform miracles in this reality. Standing in front of his self-portrait in his royal chamber, he reflects on his past:
He contemplated his portrait. He had portrayed himself as a teenager
with short hair, with lines accentuating the angles of his face. He
had conceived this painting by trying to remember an old photo ID
formerly taken for the Wotan project file. His candidacy had been
favorably received. He had become a computer man.
Wotan was a gigantic
computer gathering all of the world's data banks. It was later discovered
that Wotan could give access to other strata of reality, which was globally
called the computosphere because of its property to absorb or swallow
computer programs. The computer-men, who lived in symbiosis with
Wotan, had the possibility of projecting themselves into the
computosphere. It was unclear to what extent these other universes
pre-existed Wotan; or otherwise to what extent the
simulated programs in the computer had shaped the profile of these
worlds. Some computermen had undertaken the exploration of the deepest
and most stable strata. Many had never returned ... just could not
have come back, because of what they had discovered. This was the case
of Conrad, Sir Conrad.
Sometimes, in a paradoxical reversal, he had
the impression that he never really had had an earthly life; a kind of
expired childhood, now being erased, in which the adult was unable to
recognize himself. Even if Bass-Einf was only a computed reflection, a
simulation of the universe, the real Conrad was the one who lived in
this country, painted, breathed the icy air, had enjoyed Silvanie's arms.
Sometimes, however, he was conscious of living as if out-of-place, of being
a usurper and of occupying the palace of someone else, so that one day
someone would demand that he give back what did not belong to him. He
was unable to decide between these two contradictory feelings.
Under
Silvanie's dumbfounded eye, he emptied a tube of black onto the canvas
and carefully spread the thick paint over the whole surface of the
portrait.
The story ends with Alexander the hitman killing Conrad by throwing him overboard one of the lifts going down from Bass-Einf:
"Farewell, Conrad," he said. He hurled him overboard. He did not hear
the sound of the body being crushed, miles down.
It did not matter. Farewell, Conrad he thought with sadness. If it
cheers you up, know that I will not go back.
He had made his decision, for good. Bass-Einf was now lacking a Worker
of Miracles. Tomorrow morning, Alexander would take a lift, again. To
the city of Bass-Einf.
In his mind he formed the image of a pack of cigarettes, which rolled
over the worn floor of the platform. He took the first puffs,
listening to the irregular creaking of the giant mechanisms.
