While it is true that Hemingway writes with a great economy of words and that a good many phrases reveal as much indirect information as direct information, it would not be true to suggest that if Hemingway doesn't say it, it doesn't happen, which would be a logical contradiction to economy of words and which is exactly what your question suggests:
Hemingway is famous for having a specific purpose for every word. There are three times when he writes that the old man looked at the waiter, but the waiter never looks at the old man. Why does the waiter never look at the old man?
The two waiters are the young waiter, who is in a hurry to get home and who waits on the old man, and the other waiter, who is not in a hurry and is older than the first. The story setting places them further in looking out at the terrace. They are seated together at the same table. They are both looking out at the terrace. The terrace is where the old man sits, the only one there, in the shadow of leaves thrown by an electric light. The "street" (which includes sidewalks) runs behind the terrace.
From this, the logical deduction must be that the other waiter and the younger waiter are both looking at the old man from the table. This is confirmed at the beginning: "they kept watch on him." This is further confirmed by the incident of the girl and the soldier walking on the street behind the terrace. The soldier's insignia is lit up by the "street light." Since Hemingway does value economy of words and does use literary techniques, such as parallelism, to tell his stories, it is logical to conclude that the light is the same one and that the younger waiter saw the the passers-by because he was looking at the old man, he "kept watch on him."
One of the two passages that do suggest the younger waiter did not look at the old man comes when he refuses the old man another drink:
"No. Finished." The waiter wiped the edge of the table with a towel and shook his head.
This has every indication of shear determination to remain unyielding in his refusal of more service, in his insistence that he go home early. It is early after all: "Why didn't you let him stay and drink? ... It is not half-past two." For some readers, this passage conjurers up the image of grit teeth and stern rejection and refusal to make eye-contact.
Logical deduction suggests this scene is a dramatic exception, different from an earlier one when he made rude remarks directly to the old man. If logic indicates that this was a dramatic exception, then logic also indicates that the younger waiter did look at the old man while being rude, while approaching him, while waiting on him and at his departure.
The waiter watched him go down the street, a very old man walking unsteadily but with dignity.
In light of this, it might be better ask: Why he did not look at him then, when insisting on putting himself first and going home early? It might be better to ask: Why did Hemingway make a point of stating that the old man looked at the younger waiter?