You cannot register your already bought game at gog you have to specifically buy it from them to get their updated client.
There wont be such option since Blizzard ditched the title and abandoned all support for the game.
Blizzard can never sell the game in that state it does not meet their standards they would have to fix it.
Basically gog is asking players to pay for what fans already did for free and what should have been done by blizzard a long time ago if they did not abandon the game...
Now lets imagine that blizzard was the one doing it and not gog for a second, take a game people already have bought, fix the bare minimum for it to barely work again and charge the full game all over again to it's customers in order for them to just have exactly the same experience they had before.
You effectively are making people pay for customer support on a product they already bought we are not talking additional content or expansion here just keeping the product barely working.
I know most people are fine paying for what should be free but not everyone is a mac user
Now if blizzard or gog was to make a re-master of the game which means upgrading the textures, adding match-making, greater battle.net support, etc... that would be another story they can sell that this is content but keeping a game working is not something we should encourage selling.
Look at war3 they are doing a remaster and it is looking good because at the same time they keep the old game working as well they update it they did not abandon it they only make you pay for the new graphics and new content but keeping the game working is not something they charge you for and that should never be...
so yes for me gog is just a scam in disguise...