Is it exploitation? I'd argue slave or prison labor is exploitation because the workers have no freedom of choice. Bees are free to leave, and the queen will in fact do so if not content with the conditions in the hive. If the queen leaves, all of the bees will swarm with her and you'd be left with an empty box.
Beekeeping strikes me more as symbiosis. The beekeeper provides ideal conditions, far better than the average location that would be found in the wild, and can help protect the hive against threats like mites. In exchange the beekeeper receives a share of the honey produced by the hive.
No beekeeper takes all of the honey from the hive. Only the top box (the "honey super") of a typical hive stack is harvested. A grate below the top box (a "queen excluder") prevents the queen from entering it so no larva are laid in the top box. The workers bee are smaller and can pass through the grate to build out comb and produce honey. The comb and honey in the bottom boxes are left to the hive to feed its workers and produce the next generation of bees, ensuring the survival of the hive.
A queen excluder cannot be used to prevent swarming long-term as the drones that gather the pollen also won't for through the grate! An excluder might be used to delay swarming and buy time so the beekeeper can offer another solution, like adding more boxes to the hive or splitting it into two hives. Better beekeepers proactively manage their hives, e.g. by setting up an empty hive in advance to essentially offer a swarming hive a new ideal home whenever they're ready for it.
Watching Skill Up's review now, and oof. That art style... that writing. Don't know who they made this game for, but it's definitely not me.