It's a trivial question most PC gamers will have pondered at one time or another, as upon booting up a new (or, more importantly, old) game bought from Steam, they have to wait while DirectX installs. Again. For, like, the 100th time.
Turns out it's not a Steam error. It's just the price you pay for having such a unified service on a platform as disparate as the personal computer.
Valve say that because of the way DirectX is used for individual titles, and because of the way Microsoft has configured the code to install itself, it's incredibly difficult to pack only the files a game actually needs inside its installer. So Steam just installs/reinstalls the necessary version every time you first play a new game.
This means it doesn't matter if you've just played a game from 2011; if you then install a game made in 2009, you'll still need to install DirectX once again, even though you've got a "newer" version already on your system.
That's of course the abridged reason; for the full technical rundown on why it's so, check out Valve's explanation at the link below!
Steam Forums [Steam]