Edit 4/4/2014: Hey OP, look at what was just released today:
I just wanted to expand a little on the accepted answer, because it's a little sparse on details. Filipe's answer makes no mention of the strategies that Windows actually does use to resolve or mitigate program dependency issues, like the component store (WinSxS,) the global assembly cache, the MSI system, etc. But on the other hand he's basically right in the sense that it's the developer's responsibility to include any custom libraries with the app, and check for the existence of dependencies before committing to the install transaction.
Windows is less modular than Linux, which has positives and negatives. On the down side, Windows is more monolithic, meaning comparatively fewer components of the operating system are removable or optional like in Linux. (Though Windows is slowly getting better about that.)
But on the up side, that means developers are able to make a lot more assumptions about what libraries a user will already have present on his or her machine. And various versions of those libraries, once installed, will be stored side by side in the component store, so that you no longer have App1 barking about needing crapDLL.dll, and App2 barking about needing a different version of crapDLL.dll at the same time, etc.