Yes it does. Don't know why they did GWG for Great Western Green, and not GWR for Great Western Railway though. Would've made more sense IMO.
On the same subject, what does BLG stand for after the class 101? I guess it refers to the livery like the other trains, but I can't think of anything that fits those letters.
In case Great Western come up with a silver livery or something in the future. That would then be GWS and distinguish two Great Western Railway liveries in the game. In the same way, the different CSX liveries aren’t all just called CSX, as there would be no way to distinguish them.
I have a feeling it may actually be something internal in case they add extra liveries for that train and that route (like the GWE Class 66, which was originally only in DB Red).