This is not an accurate prayer for lighting the shabbos candles, but that would be very strange, and disrespectful to put on Broadway. However, it is strange that it elects to name Ruth and Esther (known for their obedience to Gd, but not for being matriarchs, who are normally named if women are named in Jewish prayer).  

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Nevertheless, the prayer -and Golde specifically lighting the candles- as well as the rush to make sure everything is ready, is a good reminder of a lot of religious Jewish weekly life. 

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It is worth noting that while Tevye and Golde sing together, traditionally the wife lights the candles and says the blessing. Additionally, she will draw her hands around the lights of the candles and cover her eyes, typically three times, but anywhere from 1 to 7. 

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At least two candles will be lit for a couple, but some people elect to add a candle for every child. More candles is never a bad thing, so long as you don't stretch too far one week. It is customary never to decrease the number of candles that are lit. 

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You can read more about the ritual of lighting the Shabbos candles here.