You *cannot *make a carbon copy of a game, and that particular quotation certainly doesn’t imply that you can. Game mechanics can be copied, game content cannot.
Thanks for all the input on this area, we already decided to make a different game, keeping some gameplay core concepts present of course, but different in several other areas.
No one asked to make a carbon copy. If they had, my response would have been different. 
He wants to make a remake and a remake sounds at least for me… that you are using the same name “which is usually also protected “copyright” .” and you are not only creating a clone but more a copy of everything, story, characters, names, game content, levels, storry etc… And this is of course not legal… It’s really funny that some people think they can do what because it is free r a remake. Like i wrote lets make a “reamke” of “The Divison” or just make a free to play copy of Epics “Fortnite” i think you will hear pretty quick from them and definitly not in a positiv way…)
@Artemix, i think this is the best solution… 
at least the one with no stress and fear about copyright and no cost for lawyers
This is really a great community, no question about that but for questions like this ask a qualified “real” lawyer, the internet is full of wrong claims and you will get alwys like 1000000 different answers…
Its really simple. It doesn’t work for mods, it won’t work for a free standalone game. There is no way around it unless you get written consent from the current license holder. (It may sound scary, but depending on the game, you may actually get a chance to remake it.
Funny thing is, there was a Duke Nukem 3d remake, “Duke Nukem 3d: Reloaded” by Fresch and his team. The project was put on hold because of a dispute with Gearbox Software. Now he runs his own company called Interceptor Entertainment and with the help key staff from the original 3d Realms, brought 3d Realms back from the dead. So even if the response from the license holders may sound unusual or down right stupid. You just have to have the right intentions and people at your side. The craziest things could happen.
In the end, just make inquiries before putting any effort into it. I get away with a lot of “Remakes” because i’m developing for my portfolio as prototypes and only accessible by me and specific contacts and (if allowed by my contacts) view-able and maybe playable on my website…I doubt that would be your intentions here though.
So don’t be put off by the idea of denial. Look at it as an opportunity that “Can” happen with potential to fail. Failure isn’t always a bad thing.
Sounds pretty clear they originally wanted to make a copy to me 
Yes, the original idea was to make a copy, also as a sort of “tribute”, even if the original makers didn’t think that way.
But since there could be issues, I will only keep the core gameplay aspect, and remake everything else.
Try to contact the owners of the game and get permission - this is the best way.
…My point is…No one is going to hassle you for making a flappy bird or other game and changing only the content. I could go on and on and in multiple platforms in which developers have stolen each others gameplay 100% but have changed content. If you grew up at all in video game history you will have seen your fair share of complete and utter ripoffs, that have made you go, wait a tick… and those titles are even being sold, which is totally legal.
However when you see a game like Pokemon and a fan does a remake, the reason they get C&D letters is because they are using trademarked images or content from other pokemon video games themselves. Making it illegal. You will never see Digimon get C&D letters because they have transforming monsters, just like pokemon.
You cannot legally C&D someone for making a similar game. They can try, but i guarantee you if the game is 100% free of infringement you will win.
As long as the game you have made has 100% nothing from the original developer, ie content. You can copy the gameplay 100%.
I present the first ever legal video game ripoff.
Pong.
It was stolen from Table Tenis on the Odyssey.
Magnavox even tried suing Atari. Yet settled out of court. Granted this isnt an example. Since they stole everything, even the controller scheme. But there you have it, even Atari.
A better example would be Fighter’s History, a rip-off of Street Fighter II or MaXplosion VS Splosion Man. An even better example would be the entire company of Zynga
I’m not saying you should, but it’s not illegal.