I've had a quick look, but am not aware of which file the version check is in. (and didn't know about it being done last year, so didn't search for prior knowledge)
OK, this method allows the 8.1 Preview RSAT to install on 8.1 RTM Download the language pack ISO for Windows 8.1 and mount it. Then in PowerShell, run Add-WindowsPackage -packagePath I:\langpacks\en-us\lp.cab -online (substitute I: for whatever drive letter the image is mounted on). Once it's finished, try the update again.
Weird, the preview RSAT has installed just fine on every 8.1 RTM I have tried it on, with no special steps or anything.
same here, I just loaded the enterprise rtm and used the set from the 8.1 preview and it installed without any tricks