Well, Return to Castle Wolfenstein mostly doesn’t take place in a castle, except for a few levels. You’re a WWII soldier fighting Nazis, zombies, and Nazi zombies. The titular castle is the headquarters of Nazi-zombie research. It only shows up in the first level, and the last few levels (when you return to it). The castle is riddled with hidden treasure rooms filled with Nazi gold, though, so there is a treasure hunt aspect to it, and it’s a pretty good game for running through a castle in a first-person perspective, albeit one that’s mostly filled with swastikas and Nazi super-science. This is a pretty good example for your paper, so long as the 20th century setting isn’t a problem.
The Elder Scrolls games are mostly Generic European Fantasy Setting games. They’re “open world,” which means they give you an entire countryside you can wander around in, populated by towns, villages, guard towers, dungeons, lairs, and, yes, castles. Castles are mostly places you go to get quests from the local lords, although, given the open world design, they can also be places you go to steal everything that isn’t nailed down, or to slaughter everything that moves, if that’s the sort of thing that strikes your fancy.
I haven’t played Final Fantasy VI, but my understanding is that it’s not a medieval fantasy setting, but more of a magic/steampunk thing. I’m not sure how much a role castles play in it.
For more directly castle-themed games… well, there’s always the Castles series of games, wherein the player designs and builds a series of castles, defends them from attackers, and uses them as his seat of government for resolving important plot points related to the governing of his realm. The castle design part of the game was fairly innovative at the time, but was limited by computing power and AI sophistication - the best castle designs in the game were, IIRC, utterly impractical as real-world designs.
There’s also the Total Wargames, two of which were set in medieval Europe, two in feudal Japan, one in Napoleonic Europe, and one (soon to be two) in ancient Rome. The Japanese and medieval European ones feature a lot of castle action. In these games, you’re ruler of a feudal state, and are trying to amass as large an empire as possible, through a mixture of diplomacy, espionage, and open combat. Mostly, open combat. Each region can have either a castle or a city in it, and conquering a region requires conquering the region’s capital city/castle. The sieges can be pretty detailed, include knocking down the walls with catapults or scaling them with ladders and siege towers, and the game puts you in the position of both attacking and defending, depending on how well the the strategic game is going for you.