It depends
The confection — the twists and ropes — is typically bound with wheat flour. Licorice root and licorice extract used as a flavoring are a different thing and are gluten-free.
Two unrelated things sharing a name. Licorice root is a plant, and the extract taken from it is a flavouring that appears in sweets, teas, tobacco and some medicines. Licorice the confection — the twists, ropes and bootlaces — is a flour-based candy that happens to be flavoured with it, or in the case of most red licorice, not flavoured with it at all.
Because the sweet is wheat and almost nobody expects it to be. It is chewy rather than crunchy, it is sold with the gummies rather than the biscuits, and the thing it is named after is a root. Wheat flour is the binder that gives it that texture, which means it is not an additive that could be swapped — it is structural.
Red licorice counts. It contains no licorice at all and is still made the same way, from enriched wheat flour, so the name misleads in both directions at once. Gluten-free licorice confections do exist and are usually built on rice flour or tapioca, and they say so prominently because it is their entire selling point.
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.
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 the full nutrition panel. 360,000+ packaged foods are already read and waiting.
The aisle guides below cover Licorice 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.