Little inferno is more of an passive experience rather than a game. You spend a majority of the game burning items you buy from a company called the "Tomorrow Corporation (TC)". The TC has a dystopia nature. Everyone in you neighborhood has a fireplace and burns items from the TC and doesn't go outside in fear of freezing in the snow. There are many themes of consumerism throughout the game and it shows the pitfalls of over-consumption. The most mature part about the game perhaps is the burning, which may cause kids to have an itch to start a fire. The items you will burn range from a number of household items such as toys and kitchen utensils. For the most part, nothing you burn is alive (except for some bugs and fish); although what your protagonist burns isn't safe. You can burn the fuse of a bomb, a package of batteries, a chainsaw, and many other dangerous items without consequences. However, as the story progresses, your neighbor who constantly sends letters to you has an accident with her fire place and nearly dies. Apart from that, you can burn liquor and some pharmacy drugs, although you can never consume these yourself. There is a toy you can burn called "low self esteem action doll" who carries a bottle of wine and says "come here boys" in a drunk voice, but doesn't wear anything revealing. There is a but if crude humor here too. You can burn a toy named "kitty kitty poo poo" that shoots out black pellets when it is burned. Thats pretty much all the mature content you will find here. Make sure your child knows the consequences of burning things in real life.
(Side Note: One parent made a comment about burning children in a school bus. You can buy a small toy called "party bus" that has dolls in it. For comic effect, a sound of screaming children is triggered when the toy is burned. It's a little morbid, but nothing alive other than bugs are burned in this game)