You really should be using Microsoft.Net.Http
from NuGet, which is a Portable Class Library from Microsoft that brings the HttpClient methods from .NET 4.5 to all current versions of the Framework, and includes GZIP and DEFLATE support.
It would also mean that all of your code for the function you are attempting to complete would stay the same, no matter what platform you are targeting.
I should also point out that the code you are using will work when the stream is actually GZIP encoded, but will not work if the stream is not compressed. Which is all the more reason you should be using HttpClient.
HTH