Eden: The Game is the official video game for the TV series Eden, and it puts you into a very similar situation. You're in charge of a community of survivors stuck on a desert island where you have to raise buildings, hunt for animals, harvest crops, etc.
To make your small community prosper you have to erect different types of buildings: shelters, warehouses, kitchens, workshops, etc. As you build new buildings you can carry out a wider variety of actions. The workshop, for example, lets you build new tools or decorative items like statues. You can even build roads.
One of the most important elements in Eden: The Game is how you manage your resources – water, wood, rocks, and meat. You have to do it well because they're limited, and if you run out you won't be able to attract new survivors to your camp.
Eden: The Game is a really fun survival game with tons of content. Its low-poly visual style is also great.