Monmusu Island

A curse has gutted the island, so its monster girls do the sensible thing and summon a summoner-shaped idiot to fix it, because ancient magic apparently had no better options. He's perverted, oblivious, and exactly the wrong tool for the job, which is the joke.

The plot is thin on purpose: the island is dying, the girls need help, you're it. Everything else is played for laughs rather than lore.

You click through the island point-and-click style, tending to it and its residents in an idle management loop while the girls' attention turns from the ruined scenery to the fool who showed up to save it. Progress unlocks their trust, and their trust unlocks the rest, handled through short animated scenes rather than any real choice-and-consequence system.