R3 is a significant departure from the previous SDKs in the way that it is structured. From R3 onwards, the SDK is modular instead of having everything in one large package. The aim of this is to reduce the install size of the SDK by not forcing people to download functions that they will never use.
You need to install the Essentials module first and then the additional modules that you require for your project. If you want the full SDK then download and install all of the listed modules. As you observed, there is not an option to download a full R3 package on the download page that you have been using.
The R3 SDK modules are all in the 'SDK Components Download' section halfway down the download page.