I started a game of Civilisation V with God & Kings expansion (GOTY edition, so a bunch of DLC as well). Started as Genghis Khan and warred a bit for prospective expansion areas, gaining an enemy capital, that I happily annexed. Then I turned my eye towards neighbouring city-states aiming to claim their luxury resources by conquering and puppeting them, but to no avail. Game didn't prompt me for choice, as I entered the city with my infantry, it immediately became annexed. Now I cannot raze or puppet the captured city-state. Why? Is this a game bug?
No, it is not a game bug. The game does not allow you to puppet an enemy capital once you capture it. Since a City State has only one city, that city is considered as their capital. Hence you cannot puppet a city state, in most cases.