Choreographer Justin Peck grew up with “West Side Story.” The son of a New York City father and an Argentine immigrant mother, he was first shown the 1961 movie musical when he was very young — the family by then lived in California, and Peck thinks his parents were feeling nostalgic. “I was so enamored by what I witnessed,” Peck said, in a Zoom interview earlier this month. “Seeing men perform and express themselves through movement was something I couldn’t fully comprehend, but something I knew I wanted to seek out.” He studied dance, came to New York at 15, and eventually be...