According to the narrator of "Dusk," who does the dusk hour belong to?

Dusk is defined as the darkest period of twilight. According to the narrator of Saki's story "Dusk," the time was about six-thirty in early March. At that time of day and at that time of the year it would be getting quite dark in a northern place like London. The narrator devotes a whole paragraph to describing the people who haunt the park at that hour, as viewed by Norman Gortsby.

Dusk, to his mind, was the hour of the defeated. Men and women, who had fought and lost, who hid their fallen fortunes and dead hopes as far as possible from the scrutiny of the curious, came forth in this hour of gloaming, when their shabby clothes and bowed shoulders and unhappy eyes might pass unnoticed, or, at any rate, unrecognised.

Gortsby himself identifies with these people.

He was in the mood to count himself among the defeated. Money troubles did not press on him; had he so wished he could have strolled into the thoroughfares of light and noise, and taken his place among the jostling ranks of those who enjoyed prosperity or struggled for it. He had failed in a more subtle ambition, and for the moment he was heartsore and disillusioned, and not disinclined to take a certain cynical pleasure in observing and labelling his fellow wanderers as they went their ways in the dark stretches between the lamp-lights.

The young man who sits on the bench beside Gortsby stands out in contrast to all the others in the park. He presents himself as a country gentleman who has plenty of money but is temporarily financially embarrassed because he left almost all of it in his hotel room and now can't find his hotel. His story is intended to make Gortsby believe that he might be able to make a friend of a man who is of a superior social class, because the young grifter tells him he doesn't know a soul in London. These words from his hard-luck story have been carefully crafted.

"There's a nice predicament for a fellow who hasn't any friends or connections in London!"

Obviously, he would be deeply grateful if Gortsby could lend him a little money. He might show his appreciation by inviting Gortsby to dinner when he found his hotel, and he might even invite him down to his parents' estate for shooting or riding. All of this is implied, not stated.
Gortsby is cynical. But when he finds the cake of soap on the ground near the bench, he goes rushing after the hustler and apologetically offers him the loan of a sovereign to get him through the night at a different hotel.
The point of Saki's story is that many people seem glad to lend a hand to those above them on the social ladder but reluctant to help those who are really in dire need. This truth is illustrated in Mark Twain's story "The Million Pound Bank Note" and in "The Umbrella Man" by Roald Dahl.