I would like to know if the PayPal REST API Support Desktop/Installed Apps?
When I go to create a new application the only two options for Integration type are 'Web' or 'Mobile SDK'.
You can use the Integration Type as Web and use any of the .NET SDKs available here to build Windows Desktop Apps.
http://paypal.github.io/#payments-tab-csharp
Let us know if you are looking for Windows 8 version of the SDK (as this is currently under development).