Well maybe some .bat file would make it open through GOG. But I am not a programer so I have no skill to make such thing. I think it would be required to make GOG see corsixTH exe as it was exe file which GOG use to open the game.
If corsix creators would be kind then they could make it :)
But as for CorsixTH itself I noticed there is few things still lacking. Like other hospital scores are not working at all.
I'm not sure that we can make that link work on our side - you would either have to replace the executable that GOG Galaxy runs, or if you are GOG maybe make custom launchers an option?
And yes there are a few things lacking. Coincidentally there is work in progress on the other hospital scoring. Multiplayer is still a long way off (unless someone champions it - who is willing to do a LOT of work.) Rat shooting and demo levels are sadly still missing :-(
If anyone wants to help us out; we are a friendly and welcoming community!