While not entirely Puerto Rican, the song has distinctly Latin tones that make it kind of a generic Hispanic song. It doesn't entirely embrace Puerto Rican culture specifically, but groups the Puerto Ricans in with Mexicans and other Hispanic cultures as a whole. This was not uncommon for the 1950s, and is still not uncommon today, as American society has had a lack of interest in distinguishing between the different nuances of distinct Hispanic nationalities and cultures, and the dance in "West Side Story" reflects this.
Another example of how dance presents a cultural identity on stage in America is the musical "Fiddler on the Roof." This play focuses on a Jewish Russian community in the 19th century. The play is nothing but cultural references to the Russian Jewish people of this time period, including clothing, dialogue, and dance. The concept of the fiddler on the roof, the traditional Russian dancing during the songs "Tradition" and "To Life" are all very accurate. Rather than stereotyping the whole community under one umbrella of a generic, similar cultural heritage, such as was done with the Puerto Ricans being generalized with all Hispanics in "West Side Story," "Fiddler on the Roof" accurately and rather sensitively for its time, portrays the 19th century Russian Jewish community as far as their culture goes, and this includes the traditional dancing incorporated into the play. It is not modern dance, and can in no way be considered American; rather, it transports the viewer back in time to 19th century Russia into a community of Jewish people and shows them as they are, with their traditional dances and music (this includes the squatting, jumping, and kicking moves that are so closely identified in Russian dancing).
Finally, the musical "South Pacific" incorporates both American and Polynesian elements in its storyline, its music, as well as its dance. This is a hybrid musical, and was written about the same time (mid-20th century) as "West Side Story" and "Fiddler on the Roof." What makes it a hybrid is that it is about American people in a non-American setting, and as such, there are non-American people in the play (the Polynesians). While many of the song and dance numbers are distinctly American in nature, i.e., more modern and upbeat, there are a few numbers that attempt to be "island" in sound and movement, such as "Dites Moi" and "Bali Hai." The first song is really just a children's song sung in the French the Polynesians used at the time, without much dancing. However, "Bali Hai," though a solo, involves a lot of what is considered to be traditionally Polynesian movements, such as swaying of the hips, undulating of the arms, and wave-like movement of the belly. The play itself does stereotype the Polynesians (the shyness around men of Bloody Mary's daughter, her exotic alluring nature, the pidgin English of Bloody Mary herself, etc.) to a certain extent. The stereotypes are based on the accounts of American soldiers of their interactions with the Polynesians during WWII. Some of the actual culture of the Polynesians got lost in the translation in the telling of these stories, so what you see on the stage in terms of portrayal and dance is a mix of what the Polynesians actually were at that time and the American soldiers' re-imagining of them.
While "Fiddler on the Roof" has little to do with the American identity other than that it is an American imagining of 19th century Russian Jewish culture (based on research that made it largely authentic), "West Side Story" and "South Pacific" blend mid-20th century American ideas and ways of life into the cultural representations of Puerto Ricans and Polynesians of the period. While there is definitely some mis-representation and stereotyping going on, as these plays were written in the days before the Civil Rights movement and cultural equality really took off, looking at them today, and at the dances they incorporate using both American and non-American characters, the audience member gets a very good and accurate representation of the overall American identity as a nation in the 1940s through 1960s.