Last week I upgraded my Windows Github to Github Desktop.
It is certainly a lot faster than that last update they made for Github Windows. It also has a nice little visu
I personally confirmed that, on the new version, advanced branch management has been removed, and you can only delete branches from the website.
As a personal recommendation, you should give Atlassian SourceTree a try. Works like a charm, it's free (requires a free registration), and even when it's originally developed to work with Atlassian's BitBucket repositories, it also works well with GitHub.
And BTW, with SourceTree, you can remove GitHub branches :)
Hope it helps!