It depends on the social maturity of the child, as well as with the game.
If the child is very social and will likely be playing the game with a lot of -different- people, then I would say yes. If child is able to express themselves in a very unique and personal way, then again yes. But if the child is going to be playing the game with the same couple people in the same exact way, and there's no way for significant variation to occur during which the child remains the focal point, then I would lean toward no.
Here's some examples:
If a child will be able to play monopoly with his siblings, and with his friends from school, and with his friends from soccer, and with his friends on the block, then he will constantly be experiencing something different. He will view this gift as clearly for him.
If a child will be able to play Magic the Gathering with his siblings, and can spend a lot of time building and customizing his deck to play with, he will be able to express himself creatively. His siblings will be doing the same, naturally, but generally that will be out of sight and out of mind. He will view this gift as clearly for him.
If a child will be able to play monopoly with his siblings, but you all live too far from town to really have many friends over to mix things up, this would probably be viewed as more of a family present.