For those who are just trying to check for updates to their applications on a surface device running Windows 8.1 RTM, I at least found a workaround.
You can manually deploy your package to your device by processing the package contents on a USB drive and running the already installed powershell deployment script.
Basically, you need to start the process of creating a normal package, which you do for deployment in the application store, to create a package, and then copy the contents of the package folder (not the compression package itself) to your USB drive. This folder should have a file named Add-AppDevPackage.ps1 .
Open the USB device from Surface RT, right-click the Add-AppDevPackage.ps1 and select Run Using PowerShell. You will receive some confirmation prompts on the command line and a popup window asking you to start with administrator rights.
This is by no means a convenient or quick process, but it worked for my purposes.
This link contains more information on manually deploying your application package.
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