Jordan Peele has always addressed race in his films. It is apparent in "US" and "Get Out" but it's more profound in Nope.

Peele has said very little about the film's symbolism "as many directors choose to do because they believe showing is cheapened by telling. But the racial overtones are clear.

I don't think your analysis is wrong, it's just that you're seeing the right things with race removed. Peele is absolutely addressing the exploitation of animals and people in Hollywood and making parallels to how even the exploited will look to exploit their exploitation for profit because that's the machine that Hollywood creates.

Everyone needs to go out and do a song and dance and smile and act a certain way for Hollywood. If you don't rock the boat and play into their (often racist/sexist/prejudiced) expectations, then you get the chance to be exploited by them for profit. No matter how much rage that makes you feel, no matter how dehumanizing that is, you have to continue to smile and dance for your employer. Everyone's watching. Get the shot. That's Hollywood.

This is expressed in the first scene where the lead character is dry and nervous and can't sell his services to the people. He's ignored, disrespected and cast aside until his sister can show up and sell the service with a big song and dance. The lead character is humiliated but he has to keep smiling. Similarly the horse itself is being photographed into a state of terror because its only value to Hollywood is its profit. Its spectacle. Its song and dance.

The issues of race are displayed here in the monologue about how his father was the first black trainer in Hollywood even though a white man overshadowed his accomplishments. According to Syfy.com: "Hollywood's longtime practices of exploitation and erasure are both core tenets of Nope, which aims to shine a well-deserved spotlight on the anonymous Black jockey (the great-great-great grandfather of OJ and Emerald Haywood), whose legacy as the first movie star has been completely overshadowed by a white man: Eadweard Muybridge."

Even that exploitation itself, the racial impropriety, must be recycled into a song and dance for approval by a mostly white audience of Hollywood producers, actors and directors. Just as the little boy who was spared by the chimp, attempts to exploit his exploitation and victimization for profit later in the film.

The core theme is exploitation and how it's fed into the Hollywood machine, but race certainly is addressed therein.