Closing down does not necessarily mean that the player will make a tackle. This can happen when the player is not the type who "dives into tackles".
Closing down is not for the sole purpose of tackling and getting the ball. Its main purpose is to force the opposing player to go wide, force them to make passes to other players away from your half (and hopefully make a bad pass). If your player can take the ball away, its good. But if not, then at least they force the opp. player away from making attacking passes.