It depends
Because the answer depends on the rest of the label, scanning the actual product is the only way to resolve it — CiCi checks for a gluten-free claim, the allergen statement, and which agency regulates that label, then tells you which way it lands.
hoisin sauce is one of the names CiCi tracks for Oyster sauce. Ingredient lists use many names for the same thing, which is a large part of why gluten slips past careful readers.
Every one of these is the same ingredient. The number of names is a large part of why gluten slips past people who read every label.
Point CiCi at the barcode on the product you're holding and get this same reasoning in about two seconds, plus the carbs and whether it has been recalled. 360,000+ packaged foods are already read and waiting.
The aisle guides below cover hoisin sauce in context — which is usually the more useful question, because an ingredient rarely appears alone.
This answer comes from CiCi's ingredient lexicon — the same rules the scanner uses, not a separate article. Where reputable sources disagree, CiCi takes the conservative position and says so.