You can get away with 2x2 shacks, or 3x3 shacks later in game.
You need a roof over your head for:
- Crafting new gear at a crafting bench or repairing your gear (building a boat requires a workbench nearby etc too)
- - (Same applies for the Forge)
- Setting a bed as your spawn point for when you die and respawn, and using it to skip night time (also requires a lit fire nearby)
- and when it rains, having a roof over a fire (with proper ventilation for the smoke) will keep it lit and functional.

Other constructs will be needed arm and feed yourself:
- Cooking rack on top of a fire to cook meats.
- Cooking pots on top of a fire to cook better food buff items.
- Smelter to smelt ores into metal
- Storage chests to keep materials.

Etc, etc, etc.

You might not NEED to build to beat the game, but some essential items will certainly make the game easier to beat.

Also! you can play with others online, so if you don't want to build, play with someone who likes building, and they'll take care of it for ya while they enjoy your love of killing stuff (which they might need help with themselves)