It's because he doesn't "see" them for he doesn’t care about them and this lack of recognition shatters the very existence of people who only define themselves through others.
This cuts right down to the core theme of the novel and the primary aspect of Howard Roark's character, which is that he just doesn't give a damn what other people think about him or his work. Compare to one of the earliest scenes of him walking the streets of Stanton in Part 1, Chapter 1:
People turned to look at Howard Roark as he passed. Some remained staring after him with sudden resentment. They could give no reason for it: it was an instinct his presence awakened in most people. Howard Roark saw no one. For him, the streets were empty. He could have walked there naked without concern...
He repeatedly exclaims that he follows his vision for his own sake or rather that he does what he thinks is best and doesn't let others judge that for him. He goes about shaping the world around him on his own terms and without compromise. In the way the novel intends to make a case for individualism and independence, Howard Roark is the embodiment of that ideal. To say it with his own words during the Cortlandt trial in Part 4, Chapter 18:
"I came here to say that I do not recognize anyone’s right to one minute of my life. Nor to any part of my energy. Nor to any achievement of mine. No matter who makes the claim, how large their number or how great their need.
"I wished to come here and say that I am a man who does not exist for others.
"It had to be said. The world is perishing from an orgy of self-sacrificing.
Now first of all, speaking with a little vest-pocket psychology, a personal part of this is that he is also often described as calm and concentrating on himself and his work, without being too much into hollow chit-chat or disingenuous politeness (which is also part of why he struggles with the business side of his trade at the beginning). He is honest, straight-to-the-point and matter-of-fact. So not seeing much of others is part of how the novel transports Howard Roark's focus and determination.
Another aspect that adds into this is that there probably isn't much of substance for him to see in many people anyway, in the sense that for him they lack somewhat of a personality of their own. We see this when he meets possible clients early after opening his own office in Part 1, Chapter 13, many of which are presented as only wanting what others determined for them and thus according to him lacking their own character:
He tried to explain and to convince. He knew, while he spoke, that it was useless, because his words sounded as if they were hitting a vacuum. There was no such person as Mrs. Wayne Wilmot; there was only a shell containing the opinions of her friends, the picture postcards she had seen, the novels of country squires she had read; it was this that he had to address, this immateriality which could not hear him or answer, deaf and impersonal like a wad of cotton.
Mr. Mundy listened blankly. And Roark felt again a bewildered helplessness before unreality: there was no such person as Mr. Mundy; there were only the remnants, long dead, of the people who had inhabited the Randolph place; one could not plead with remnants or convince them.
But he doesn’t dislike or resent them for their lack of integrity, there's just nothing of interest for him there and nothing to get from them. He just doesn't care. This indifference is also expressed in his confrontation with Toohey in Part 2, Chapter 15 (and contrasted to Toohey himself who is eager to know what others think of him):
"Mr. Roark, we’re alone here. Why don’t you tell me what you think of me? In any words you wish. No one will hear us."
"But I don’t think of you."
So metaphorically speaking he really doesn't see a lot of these people. He sees what he wants and needs to see. But this goes even further when we consider that this isn't just about him not seeing them, but even more so them feeling not being seen by him. And this idea of making his surroundings feel unseen or nonexistent is also picked up again in the effect he has on his eventual coworkers in Part 1, Chapter 4, where it adds it into the larger significance Roark has as an individualist and why everyone else hates that and works against it. He himself is a presence that tends to intimidate people with less of a strong individual personality than his, thereby overshadowing their presence.
Both men disliked Roark. He was usually disliked, from the first sight of his face, anywhere he went. His face was closed like the door of a safety vault; things locked in safety vaults are valuable; men did not care to feel that. He was a cold, disquieting presence in the room; his presence had a strange quality: it made itself felt and yet it made them feel that he was not there; or perhaps that he was and they weren’t.
So he doesn't see those people because on the one hand they don't matter to him but also because their lack of individualism makes them disappear against his own presence. This is a large part of why people like Peter Keating hate him and want to see him fail, he supposedly reminds the lesser men of that fact and makes them feel insignificant. He makes everyone else resent the integrity he has for they don't have it.
And this also relates back to the topic of individualism and the idea of "second-handers" who live only through others and their opinions and are thereby the antithesis to Howard Roark's independence. They seek themselves in him, but don't find anything. The majority of people around him constantly need to see their own existence reflected in others but in Roark it isn't since he doesn't care about them. They don't exactly feel unseen, they feel unrecognized. His conversation with Gail Wynand on his yacht in Part 4, Chapter 11 sums up this idea:
"That, precisely, is the deadliness of second-handers. They have no concern for facts, ideas, work. They’re concerned only with people. They don’t ask: ’Is this true?’ They ask: ’Is this what others think is true?’ Not to judge, but to repeat. Not to do, but to give the impression of doing. Not creation, but show. [...] Their reality is not within them, but somewhere in that space which divides one human body from another. Not an entity, but a relation--anchored to nothing. That’s the emptiness I couldn’t understand in people...
"I think your second-handers understand this, try as they might not to admit it to themselves. Notice how they’ll accept anything except a man who stands alone. They recognize him at once. By instinct. There’s a special, insidious kind of hatred for him. [...] They’ve got to force their miserable little personalities on every single person they meet. The independent man kills them--because they don’t exist within him and that’s the only form of existence they know. Notice the malignant kind of resentment against any idea that propounds independence. Notice the malice toward an independent man. Look back at your own life, Howard, and at the people you’ve met. They know. They’re afraid. You’re a reproach."
And for a counter-example that also directly references this, we can contrast it with the effect he has on someone who on the one hand does matter to Howard and who on the other hand himself incorporates Roark's individualist ideals, Henry Cameron in his first meeting with Roark in Part 1, Chapter 3:
People had always lost their sense of existence in Roark’s presence; but Cameron felt suddenly that he had never been as real as in the awareness of the eyes now looking at him.
Now this answer is based solely on The Fountainhead and its characters and themes of individualism. I don't know much about Rand's broader oeuvre, the thematic of which it is supposedly to be classified into. But while we can understand the novel as part of a larger monolith of objectivist philosophy, we don't necessarily have to. Maybe the themes of individualism aren't as strong in the other works as they are in this novel. But at the end of the day, they're ultimately different characters in different novels employing different stylistic devices and nothing precludes them from simply not having the exact same traits Howard Roark has or making the same point about the people around him. But I'll leave comparative studies of Rand’s characters with regards to her broader ideological framework to other answers.
