>don't enjoy beat-em-ups
Everyone's recommending the D&D arcade games because they have an inventory system to add a layer to the gameplay. Also check out River City Ransom, which adds in an RPG-ish system of money, items, and upgrades. Aliens VS Predator leans heavily into weaponry over mashing the attack button. Die Hard Arcade is similar but also has special combo attacks worth learning. Battle Circuit is a bit like RCR, but without the ability to grind. Armored Warriors lets you use defeated enemy's weapons.
Don't play generic jump-and-attack-to-win games like Simpsons, X-Men, or Oriental Legends/Knights of Valour. They are flashy but just button mashers.