I've never heard the word. But I wonder, do most English speakers understand immediately what the word means?
One Monday, Mary showed up at work with a shiner.
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Online Etymology Dictionary entry for shine offers this.
...; sense of "black eye" first recorded 1903, American English, in East Side immigrant dialect.
I am an American and I know the meaning. I think that @DonBron was dead on with his reference to hard-boiled detective fiction.
2 informal A black eye. ‘his shiner was throbbing’ ODO.
RaceYouAnytime has a point. So I used Google Ngram to compare "shiner" and "black eye". I used the default 1800-2000 year range and picked British English. In 2000, "black eye" barely edged out "shiner" (0.0000279785% vs. 0.0000311335%).
I switched to American English and "black eye" had more of a lead but not much (0.0000346592% vs. 0.0000398877%). If you allow that "most people" know what a "black eye" is then almost as many people know what a "shiner" is. That is if you believe Ngram.
There is "Shiner Beer" and "black eye contacts" so I would take Ngram with a grain of salt. I based my reply on my own sense of how rarely a word is used in my presence. While not an everyday occurrence there is nothing about "shiner" that would lead me to believe that most people wouldn't recognize it as referring to a "black eye". ODO does tag it as informal so I wouldn't assume 100% recognition either.