Yepoleb: Apart from that, everything else points in the direction of it being a closed API. Most importantly that you can't request your own OAuth credentials and have to use the ones from the official client, which is not how OAuth is supposed to work. Being able to request your own key is essential to a public API. Check out every other site on that list and you see the difference in openness.
shmerl: What did GOG say about it? Since they claimed indeed that they are supportive of community clients, how are they supposed to work?
I think it's been a long time since they've claimed that and we haven't heard them reinforce their earlier claims of supporting community made clients in a long time now. I think it is safe to say that they no longer entertain the idea of supporting community made clients nor having a publicly documented API for developers to use, and that they will restrict any APIs they do have to developers that they sign contracts to partner with at their discretion.
That's what all visible evidence appears to suggest from outside of GOG looking in anyway. If it isn't the case then it would be nice for them to be transparent about it and issue a public statement sometime soon to indicate if they are indeed dedicated to fulfilling their promise of providing a publicly documented API that 3rd parties can use for making their own clients.
IMHO, they're more likely to just maintain complete radio silence if they've had a change of heart on this and all they would have to say are things that would be of grave disappointment to the community by renegging on their prior commitments.