Genre is always complex… which makes it interesting. Oftentimes a subgenre exists because it is a melding of two genres. Action and horror seem like a natural connection.
If a hero is getting into all sorts of adventures, it seems natural that some of them involve horrifying monsters or deadly giant creatures, tropes that are closely linked to horror. For those who argue that a story is plainly just one of the genres (action OR horror) are often missing the point. Genres exist as a varied collection of tropes, and some of the best stories are a fun collection that include both horror and action tropes.
Around the 1920s pulp stories spread, and many of them in the form of what could be considered a melding of action and horror. The stories of Solomon Kane by Robert E. Howard mixed horror, action, and fantasy with tales about deadly pagans and witchcraft and a hero that could vanquish them all.
Just like in pulp stories, in many ways action-horror movies often come in the form of ones that also meld them with another genre. Usually these means either science fiction or fantasy. In the 1950s it was giant monsters or giant spiders or a pesky Creature from the Black Lagoon. In the 1970s-80s in a similar way it came in the form of Predators from another planet or meeting Aliens on a distant planet. Similarly movies like Conan the Barbarian and The Beastmaster had a lot of horror elements while still being firmly action-fantasies.