Board games: one present the whole family gets something out of
Most presents go upstairs to a bedroom after half an hour. A board game does the opposite: it comes back down, it goes on the table, and people who had no intention of joining in sit down anyway.
The age on the box is about the rules
On a toy, an age usually refers to small parts. On a game it is almost always about something else: when a child can follow how the game works, wait for a turn, and cope with losing. That is why we show it as 6+ rather than as a range — older children and adults simply join in, and with a game that is not incidental, it is the point.
Look at the player count and the playing time first
Those two numbers on the back matter more than the age. A two-player game is a different present from a six-player one, even with the same figure on the box. A twenty-minute game fits a weeknight; a ninety-minute game waits for the weekend, and comes out less often as a result.
When in doubt, shorter wins. A game played three times in an evening beats one that comes out once a month.
Four kinds of evening, four categories
We keep board games separate from card games, dice games and brain teasers, and the split is meant practically. A card game fits in a coat pocket and is explained in two minutes. A dice game has short turns and works well with mixed ages round the table. Brain teasers are usually for one player — a different kind of evening, and rarely a present to open together.
The present that includes the giver
A game is one of the few presents where the person giving it plays too. That is also the honest argument for choosing one for a child who already has plenty of toys: you are not giving another box, you are giving an evening where somebody sits down opposite them.