(sorry for bad English)
---[ Config ]---
Installer version: gog_anima_gate_of_memories_2.0.0.2.sh (latest for today)
OS: Manjaro Linux 18.0.4
GPU: Nvidia GeForce GTX 1060 6GB (driver v. 430.26)

---[ Problems ]---
1. invisible cursor both in main menu and in game. You still can select with it, blindly moving mouse and trying to highlight desired option. Switching between Stats/Skills/Items... tabs is quite difficult this way since i haven't found a keyboard way to do this.

2. Game crashes at some cut-scenes (for now in 2 spots: "The little girl runs" and after defeating Puppeteer)

---[ Plea ]---
Devs, fix this for us. I'll provide additional info, if needed for nailing down this bugs.

I don't have these issues. Instead, the graphics are completely corrupted when playing. This is one of the few games I have where playing the Windows version on wine is the only way it's playable.

I'm fairly certain the devs don't read gog's forums, and probably don't care about our problems, anyway. I recommend you try getting it working on wine as well.

Weird... Problem #1 is marked as solved on Steam forums 2,5 years ago. Whether GOG version was not patched or something changed in Linux since that times, I want to reopen this issue. I emailed link to this topic to official site 'contacts' form. And devs posted on Steam forums in Nov. 2018, so I believe we still can reach them. What stops me is my savegame I've already defeated 3 Messengers on Linux. Glancing at savegames. Seems we can't just move it to Windows. It in separate file on Linux and in registry on Windows. 'string' type on Linux and 'hex' on Windows. Seems both are base64-encoded. And on top of that windows parameters stored with some kind of hash applied to parameter name (which aren't there on Linux). I can do some scripting and write converter for everything except hashes which i can't visually recognize. Oops.

More weird stuff. "Winter" section, when approaching passage to "Portal chamber", "Nexus guard" mini boss appears. Game crashes when he shows onscreen. I installed game to my second machine (laptop, Linux Mint). Still no cursor visible, but i beated "Guard" boss... and found out that resulting savegame does not loads on my first machine now (but works on laptop). Seems I'll continue on my desktop PC without opening way to portal chamber... and hope that this issue will not emerge later on the route which I can't omit. I've backed up both saves for possible further investigation.
UPDATE: tried to go to guard second time, after obtaining 'Summer' rune and before visiting 'Druaga core'. This time system was not crashed. Anyway, I've stored the problematic save.
...
Next. "Shrine of the Seasons" location, no textures visible for ground and rocks, renders as black (checked on both machines)
...

Maybe that is sound advice.
I came here to post a similar issue on the Mac version where the corruption of the graphics make it nigh unplayable. So maybe WINE is also the answer in my case.
What a bizarre situation: Although there is a native version for the Mac, the solution may very well be from advice for another OS (Linux) using a game version re-translated from another OS (Windows).
Bizarre.

Thanks for the advice.

DRI_PRIME isn't enough, it still tries to run on the integrated graphics adapter, even though there's a Radeon card available.

Setting DRI_PRIME and using the command line option "-force-device-index 1", fixed that. Surprisingly it needs both the environment variable and the command-line option. It also needs -force-opengl, which is already supplied by GOG's start.sh

Although it starts with a GUI to choose resolution and which output to display on, that GUI doesn't allow selection of the GPU when an output can be attached to either GPU. Found the command-line option from the developer of a different Unity game complaining on Unity's forums.