I noticed after closing RCT Deluxe, that a box appears : "Please wait while Railroad Tycoon is closing". It takes a bit of time for me (about 10 seconds).

Is it due to the original game or GOG ? I admit i don't remember seeing that box in my old CDrom Version ^^

I don't remember such a thing either.
But i guess some pieces of code just got misplaced.
If it works i wouldn't care too much.

Yes it says "Railroad Tycoon" x)

The explanation is that GOG are in fact using a launcher that closes explorer.exe and reopens it upon quitting. The launcher was presumably originally made for Railroad Tycoon. Either that, or GOG made it themselves and weren't paying attention when coding it.

Perhaps you made such a good railroad ride in the game the CPU was so impressed it changed the name. It's the first-ever case of a computer gaining sentience and instead of taking over the world it's complimenting us! Seriously though, I agree it could be a typo from when coding was done.

they both use the same game engine. When RCT was in development Chris Sawyer was working on an sequel to his transport tycoon series but part way through he got an interest in roller coasters and remodeled the game in to a theme park sim. RCT 2 was the engine sightly improved to build better coasters. GOG got the source code to the engine and whent it was recompiled to run better under WinNT 6.0 an old prompt was reinstated that referenced the older title.